In an address to the nation, President Macron said: "We have so much to rebuild. Yes we will rebuild the cathedral and we will make it more beautiful and I want that to be done in five years.
"We need to work, we have to act and we will succeed. Long live the republic and long live France."
He added: "It is up to us to change this disaster into an opportunity to come together, having deeply reflected on what we have been and what we have to be and become better than we are. It is up to us to find the thread of our national project."
Watch: Paris firefighters record devastation of Notre Dame blaze (PA)
Mr Macron said he wanted the cathedral to be even "more beautiful" than before.L'Oreal, the Bettencourt Meyers family and the Bettencourt Schueller Foundation announced they will donate 200 million euros (£172.7m) towards the cost of repairs.
It comes after billionaire Bernard Arnault's family and his LVMH luxury goods group said they were donating 200 million euros to "show their solidarity at this time of national tragedy".
The iconic tourist spot was engulfed by a raging fire on Monday night that caused its main spire and roof to collapse.
A statement from the Arnault family said: "The Arnault family and the LVMH group would like to show their solidarity at this time of national tragedy, and are joining up to help rebuild this extraordinary cathedral, which is a symbol of France, of its heritage and of French unity."
The donation brings the total amount raised to more than 600 million euros, after French billionaire Francois-Henri Pinault and major French oil and gas company Total both pledged 100 million towards the reconstruction.
Mr Pinault, married to actress Salma Hayek, is quoted in French media as saying he and his father, Francois, decided to donate to help with the "complete reconstruction" of Notre Dame.
The younger Mr Pinault is chief executive of international luxury group Kering, which owns brands such as Gucci and Yves Saint Laurent, and is the president of French holding company Groupe Artemis, which owns the Christie's auction house.
Oil and gas company Total will also donate 100 million euros towards the reconstruction, CEO Patrick Pouyanne announced.
Apple CEO Tim Cook also pledged to donate to help rebuild the cathedral, writing: "We are heartbroken for the French people and those around the world for whom Notre Dame is a symbol of hope.
"Relieved that everyone is safe. Apple will be donating to the rebuilding efforts to help restore Notre Dame’s precious heritage for future generations."
Meanwhile, France's Fondation du Patrimoine, a private organisation which works to protect French heritage, said it would be starting an international appeal.
It tweeted: "For our Lady to be reborn from her ashes we are launching an international appeal. All donations received will be paid in full to the restoration site."
Mr Macron said he would be looking "beyond our borders" as the fundraising campaign got under way.
In a speech on Monday night, he said: "I am solemnly telling you tonight: this cathedral will be rebuilt by all of us together."
Describing Notre Dame as "our history" and "the epicentre of our lives", he added: "It's probably part of France's destiny and it will be our project for the years to come."
Across the pond, the US-based French Heritage Society said it would be establishing a restoration fund, while several appeals have already been set up on crowdfunding sites such as Go Fund Me and Just Giving.
A campaign launched by Dartagnans, a website dedicated to the preservation of French cultural and artistic heritage, has so far received almost £24,500 in donations from 610 users across 35 different countries.
Another, launched on website Leetchi by friends Charles Gosse and Laurent Segnis, received more than £9,500 donations in under seven hours.
“As citizens, we must all use whatever small means we have to unite,” Mr Segnis told Le Monde, confirming that all money raised on their platform would go straight to the rector of Notre Dame.
It comes after flames engulfed the world-famous cathedral on Monday afternoon, toppling its 315ft spire and threatening the entire wooden frame of the building.
The blaze, which broke out as the last crowds of tourists ended visits at around 6pm BST (7pm local time), was finally declared to be "completely under control" nearly nine hours later.
However, it is expected to take several days to completely extinguish all remaining pockets of fire, dampen down hotspots and secure the world-famous edifice.
Around 400 firefighters battled the fire into the night and tried to salvage artwork and other priceless pieces stored in the 12th-century cathedral. Paris Fire Service later confirmed that Notre Dame's structure and main works of art have been saved.
Paris mayor Anne Hidalgo tweeted her thanks to the firefighters who saved the cathedral's twin towers.
She said on Twitter: "I want to say thank you to Pompiers Paris, they saved the towers. I could not imagine Paris without the towers of Notre Dame."
On Tuesday morning, the first harrowing images from within the fire-ravaged cathedral started to emerge.
A smouldering pile of what appeared to be the charred remains of the roof and spire lay smoking in front of the altar, while a cross that had escaped destruction glowed from within the gloom.
Gilded candlesticks, artworks and furnishings were among the treasures seen being rushed from the cathedral by a "human chain" before being bundled into trucks by police officers.
Some of the cathedral's most precious objects, including a relic purported to be the crown of thorns worn by Jesus Christ on the cross, were rescued.
Marchers set off in central London earlier today with banners proclaiming "the best deal is no Brexit" and "we demand a People's Vote".
Campaign organisers said hundreds of thousands of people were in the crowd as it began to march.
The day's activities were kicked off by the unfurling of a large banner on Westminster Bridge that read "Love socialism, hate Brexit".
The stunt was organised by a group calling itself the "Left Bloc" which is supported by Labour MPs, including Clive Lewis and Kate Osamor, Green Party MP Caroline Lucas, trade unions and grassroots campaigners.
The march saw protesters process from Park Lane to Parliament Square, where a rally was held.
In Parliament Square, Labour's deputy leader Tom Watson told the crowd: "At every turn we have been ignored.
"At every stage Theresa May has doubled down rather than reaching out.
"She has made it impossible for anyone who cares about jobs, about solidarity at home and abroad, about friendship across borders and between communities to support this Brexit."
Mayor of London Sadiq Khan took to the stage to call for Article 50 to be withdrawn.
"The British people didn't vote for the government to gamble on our future, the British people didn't vote for the national nightmare that's been created," he said.
"It's time the government gave us, the British people, a final say on Brexit."
"If that is your view, Prime Minister, let the people speak," she said.
Ms Sturgeon accused Mrs May of being "in thrall to hardline Brexiteers".
She also called on Labour leader Jeremy Corbyn to back a "people's vote".
The London march coincides with pro-Brexit campaigners continuing their long hike from the North East to the capital.
Former Ukip leader Nigel Farage re-joined the ‘March to Leave’ when it set off from Linby, near Nottingham.
The demonstrations follow EU leaders agreeing to delay Brexit to give Mrs May a final chance to get her deal through Parliament.
Leaders agreed to extend Brexit to 22 May if Mrs May can get MPs to back her deal in the Commons at the third time of asking.
If the vote is not passed, the UK will have to set out an alternative way forward by 12 April, which could mean a much longer delay - with the UK required to hold elections to the European Parliament - or leaving without a deal at all.
Man presents at Tallaght Hospital after injecting himself with own bodily fluids in attempt to cure back pain
The 33-year-old presented himself at Tallaght Hospital complaining of chronic pains before telling docs he had been using his own "treatment" for the past year and a half.
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Dr Lisa Dunne of the The Irish Medical Journal detailed how the man had bought a hypodermic needle online and was injecting himself on a monthly basis, leading to fluid building up in his arm.
She wrote: "The patient disclosed that he had intravenously injected his own semen as an innovative method to treat back pain.
"He had devised this 'cure' independent of any medical advice.
"Upon further interrogation of this alternative therapy, he revealed he had injected one monthly 'dose' of semen for 18 consecutive months using a hypodermic needle which had been purchased online."
Doctors found the semen had leaked into the soft tissue of his arm, but he discharged himself a few days later without getting treatment to drain it.
Dunne went on to say it was the first ever case of its kind and warned others not to conduct medical experiments on themselves.
She said: "This patient’s back pain improved over the course of his inpatient stay and he opted to discharge himself without availing of an incision and drainage of the local collection.
"The case also demonstrates the risks involved with medical experimentation prior to extensive clinical research in the form of phased trials inclusive of safety and efficacy assessments."
But while mortality from most of the principal causes of death fell last year it increased for respiratory diseases.
Provisional figures from the Department of Health show that last year mortality rates for heart disease, strokes, non-respiratory cancers and suicide all fell.
But the number of people dying from respiratory illnesses rose slightly.
This is the eleventh edition of Health in Ireland: Key Trends published by the department.
The latest figures for life expectancy are from 2016 and are 83.6 years for women and 79.9 years for men - both are slight improvements from the previous year.
Other statistics show that while the number of acute beds in public hospitals increased it remains 10% below the 2008 level.
On waiting lists, the number of patients waiting for inpatient and day case elective procedures dropped by 24% in the 12 months from October last year - but that figure excludes people waiting for an endoscopy.
And the number of people waiting for outpatient procedures during that period rose slightly and is now over half a million - 150,000 of them have been waiting for more than a year.
The overall mortality rate has reduced by 14.9% since 2008. As seen in most European countries however, the rate of improvement in Ireland's life expectancy has begun to slow in recent years.
The report touches on several areas, including demographics, population health, hospital and primary care, health service efficiency, employment and expenditure, and highlights the significant achievements that Ireland has made for key health outcomes in the past decade.
However, it also highlights the challenges that persist in terms of the accessibility of timely and efficient healthcare across the population.
Male life expectancy in Ireland has been above the EU average over the past decade. The life expectancy at birth for men in Ireland has been consistently greater than that of the EU average by over a year. Female life expectancy in Ireland matches the EU average.
In 2016, 83% of Irish men and women rated their health as good or very good. This is the highest in the EU and compares with an average of 70% and 64% for males and females respectively across the EU.
There have been improvements seen in survival rates from breast, cervical, colon and rectal cancer in the last 15 years. However, with the exception of rectal cancer, five-year net survival rates are lower in Ireland than the average for OECD countries where data is available.
There has been a 26% reduction in the mortality rate from suicide since 2008. After a rise in the male suicide rate from 2008 to 2012, the three-year moving average has decreased and the latest figures (2015) have fallen below the EU average for the first time since 2010.
Over half of Irish men binge drink on a typical day of drinking, compared to just under 20% of women in 2018. A gender gap is present across all age groups, but the highest rate of binge drinking is among the 15-24 age group.
The number of patients waiting for an inpatient or day case hospital procedure has fallen by 24%. The total number of patients waiting over nine months for an inpatient or day case procedure has fallen by 5,300 or 24% since October 2017, to 15,523 as of Oct 2018.
The busiest time for emergency departments is 11am to 2pm on a Monday. The highest attendances to hospital emergency departments occur between 9am and 5pm on weekdays, with Monday mornings between 11am and 1pm seeing the highest attendance volumes across the week.
Less than 2% of the population donate blood. Both the number of blood donations and the percentage of blood donors in the Irish population have declined in the past 5 years. The percentage of blood donors in the population in 2017 was 1.7%.
Tanzania's LGBT community threatened with mass arrest
Paul Makonda, regional commissioner for Tanzania's main city of Dar es Salaam, announced the crackdown on Monday. He said a team would be set up to identify and arrest the "many homosexuals", who could face up to 30 years in jail.
Mr Makonda's announcement has sparked panic and fear among thousands of LGBT people in the east African nation. Some said they were too scared to go outside during the day, while others had left their homes fearing imminent arrest.
"Since Monday, I have left my place and have been moving here and there. I am always looking over my shoulder in case they coming for me," Nathan, 24, told Reuters by phone from Dar es Salaam.
"There's so much tension within the gay community at the moment. Not just in Dar, but all over the country. We are really scared. We don't know what to do and where to go."
Gay sex is illegal in Tanzania, but the law is rarely enforced. Homophobia and attacks and arrests on lesbian, gay, bisexual and transgender people have however risen since President John Magufuli's election in 2015, activists say.
Even though the clampdown is set to begin on Monday, Nathan claimed that homes were already being raided in the port city and gay people were arrested.
African countries have some of the most prohibitive colonial-era laws against homosexuality in the world. Same-sex relationships are seen as taboo and are a crime across most of the continent, with punishments ranging from imprisonment to death.
As a result, the persecution, discrimination and exploitation of Africa's sexual minorities is rife, say campaigners.
They are routinely abused, blackmailed, assaulted by mobs, or raped by police or vigilantes. Many are unable to get jobs due to their sexual identity - forcing them to sell sex through social media sites.
Tanzania has had a reputation for being more tolerant than its neighbour Uganda but, since President Magufuli came to power three years ago, campaigners say the little protection, representation and freedom LGBT people had is now being slowly eroded.
Civil society organisations supporting gay people have been shut down and activists have been arrested. Authorities have also suspended HIV/AIDS prevention programmes for gay men.
In June last year, President Magufuli said that "even cows" disapprove of homosexuality.
Mr Makonda told a news conference on Tuesday that he had already received over 5,700 messages from the public - with over 100 names of suspected gays.
A 17-member committee is also being set up, he said, which would be tasked with identifying gay people on social media sites such as Facebook and Twitter and arresting them.
Campaign group Equality Now said it was appalled and alarmed by the crackdown - which also targets sex workers. It called on the federal government to condemn Mr Makonda's statement and to enact laws and policies to protect the rights of all.
"People who are LGBT and in prostitution are already frequently ostracised and face multiple levels of violence and inequality," said Equality Now's Tsitsi Matekaire.
"Arresting them perpetuates this inequality, resulting in further marginalisation and damage to their well being."
LGBT people in Tanzania said foreign donors must pressurise the government to abandon the anti-gay campaign.
A previous crackdown on the LGBT community in 2016 was abandoned by authorities, they said, as a result of widespread condemnation by the international community.
They also called the United Nations to protect them by providing them with safety in another country.
"I haven't left my house during the day for the last four days. I am scared to death," said 19-year-old sex worker Michael, by phone from the northeastern city of Arusha.
"We have no one to protect us. We ask the United Nations and other countries to help us to go somewhere else where we do not have to hide in fear."
Michael D Higgins re-elected for second term at Áras an Uachtaráin
In his acceptance speech, President Higgins spoke of the great honour that had been bestowed upon him.
He said: "The people have made a choice as to which version of Irishness they want reflected at home and abroad.
"It is the making of hope they wish to share rather than the experience of any exploitation of division or fear."
He said his version of Ireland is one which draws on traditional genius and contemporary creativity.
"The presidency belongs not only to any one person but to the people of Ireland.
"I will be a president for all the people, for those who voted for me and those who did not.
"I am so proud of this country, I am proud to be a president for all of you and with all of you, and I look forward with joy and hope to all that we will achieve together."
Mr Higgins is the first president to be re-elected to serve a second term in office since Éamon de Valera in 1966.
Patrick Hillery and Mary McAleese were re-elected without a contest in 1983 and 2004.
Independent candidate Peter Casey finished second on 342,727 votes.
He polled more than 23% of the vote nationally, some distance ahead of the other four candidates.
Businessman Seán Gallagher secured 94,514 votes (6.4%), Sinn Féin's Liadh Ní Ríada was third on 93,987 votes (6.3%), followed by Joan Freeman on 87,908 (6%) and Gavin Duffy 32,198 (2.2%).
Taoiseach Leo Varadkar said the Presidential Election was a historic victory and a very strong endorsement for Mr Higgins.
Earlier, the Taoiseach congratulated Mr Higgins in a tweet.