Presidents, royalty and simple mourners bade farewell to Pope Francis on Saturday at a solemn funeral ceremony, where a cardinal appealed for the pontiff's legacy of caring for migrants, the downtrodden and the environment to be kept alive.

US President Donald Trump, who had clashed with the pope on those issues, sat with the rows of foreign dignitaries on one side of Francis' coffin in the vast St. Peter's Square.

On the other side sat cardinals who will pick Francis' successor at a conclave next month, deciding if the new pope should continue with the late pontiff's push for a more open Church or cede to conservatives who want to return to a more traditional papacy.

The Argentine pope, who reigned for 12 years, died at the age of 88 on Monday after suffering a stroke.

"Rich in human warmth and deeply sensitive to today's challenges, Pope Francis truly shared the anxieties, sufferings and hopes of this time," said Italian Cardinal Giovanni Battista Re, who presided over the funeral Mass.

The Vatican estimated more than 250,000 people attended the ceremony, cramming the square and the roads around.

They broke into applause when Re spoke of Francis' care for immigrants, his constant pleas for peace, the need for negotiations to end wars and the importance of addressing climate change.

They clapped loudly again at the end of the service when the ushers picked up the casket and tilted it slightly so more people could see.

Aerial views of the Vatican showed a patchwork of colours - black from the dark garb of the world's leaders, red from the vestments of some 250 cardinals, the purple worn by some of the 400 bishops and the white worn by 4,000 attending priests.

After the funeral, as the great bells of St. Peter's pealed in mourning, the coffin was placed on an open-topped popemobile and driven through the heart of Rome to St. Mary Major Basilica.

Francis, who shunned much of the pomp and privilege of the papacy during his 12-year reign, had asked to be buried there rather than in the crypt of St. Peter's, which is the traditional resting place for popes.

The burial itself was being conducted in strict privacy.

The popemobile left the Vatican from the Perugino Gate, a side entrance just yards away from the Santa Marta guesthouse where Francis had chosen to live, instead of the ornate Renaissance apartments in the papal palace.

Crowds estimated by police as numbering some 150,000 lined the 5.5-km (3.4-mile) route to St. Mary Major.

Some waved signs and others threw flowers towards the casket. They shouted "viva il papa" (long live the pope) and "ciao, Francesco" (goodbye, Francis) as the procession made its way around Rome's ancient monuments, including the Colosseum.

Trump meets Zelenskiy

The funeral provided an opportunity for Trump to have a brief meeting with Ukraine's President Volodymyr Zelenskiy, at a time when Trump is pushing for a deal to end the war in Ukraine.

In one photograph of the encounter in St. Peter's Basilica released by Zelenskiy's office, the two men sat close on red-backed chairs, leaning in towards each other in conversation.

A White House official said they had a "very productive discussion".

Among the other heads of state who attended the funeral were the presidents of Argentina, France, Gabon, Germany, the Philippines and Poland, together with the prime ministers of Britain and New Zealand, and many royals, including the king and queen of Spain.

Francis' death ushered in a meticulously planned period of transition, marked by ancient ritual, pomp and mourning. Over the past three days, around 250,000 people filed past his open coffin, laid out before the altar of the cavernous basilica.

Choirs at the funeral sang Latin hymns and prayers were recited in various languages, including Italian, Spanish, Chinese, Portuguese and Arabic, reflecting the global reach of the 1.4-billion-member Roman Catholic Church.

Many of the faithful camped out to try to secure spots at the front of the crowd, while others hurried there in the early morning.

"When I arrived at the square, tears of sadness and also joy came over me. I think I truly realised that Pope Francis had left us, and at the same time, there is joy for all he has done for the Church," said a French pilgrim, Aurelie Andre.

Farewell, 'Franciscus'

Francis, the first non-European pope for almost 13 centuries, battled to reshape the Church, siding with the poor and marginalised, while challenging wealthy nations to help migrants and reverse climate change.

"Francis left everyone a wonderful testimony of humanity, of a holy life and of universal fatherhood," said a formal summary of his papacy, written in Latin, and placed next to his body.

Traditionalists pushed back at his efforts to make the Church more transparent, while his pleas for an end to conflict, divisions and rampant capitalism often fell on deaf ears.

The pope carried his desire for greater simplicity into his funeral, having rewritten the elaborate, book-long funeral rites used previously.

He also opted to forego a centuries-old practice of burying popes in three interlocking caskets made of cypress, lead and oak. Instead, he was placed in a single, zinc-lined wooden coffin.

He will be the first pope to be buried outside the Vatican in more than a century.

His tomb has just "Franciscus", his name in Latin, inscribed on the top. A reproduction of the simple, iron-plated cross he used to wear around his neck hangs above the marble slab.

Attention will now switch to who might succeed him.

The secretive conclave is unlikely to begin before May 6, and might not start for several days after that, giving cardinals time to hold regular meetings beforehand to sum each other up and assess the state of the Church, beset by financial problems and ideological divisions.