The Vatican said 400,000 people packed St Peter's Square and lined the streets of Rome for the funeral of the first Latin American leader of the world's 1.4 billion Catholics.

After a solemn funeral, the Argentine pontiff's plain wooden coffin -- a testament to a life of humility -- was driven slowly to Rome's Santa Maria Maggiore church, where he was interred in a private ceremony.

Cardinals marked his coffin with red wax seals before it was lowered into a tomb set inside an alcove, according to images released by the Vatican.

Guatemalan Maria Vicente, 52, holding a rosary, cried as she watched the coffin being carried into Santa Maria Maggiore, the pope's favourite Roman church.

"It made me very sad. It's touching that he left us like that," she said.

The marble tomb is inscribed with just one word: "Franciscus", his papal name in Latin.

Trump was among more than 50 heads of state paying tribute to Francis, who died on Monday aged 88 after suffering a stroke.

The president met several world leaders in a corner of St Peter's Basilica before the mass, notably Ukraine's President Volodymyr Zelensky, in their first face-to-face meeting since their Oval Office clash in February.

- 'An open heart' -

Francis was "a pope among the people, with an open heart", who strove for a more compassionate, open-minded Catholic Church, said Cardinal Giovanni Battista Re who led the service.

There was applause from the masses gathered under bright blue skies as he hailed the pope's "conviction that the Church is a home for all, a home with its doors always open".

Among the mourners were many tourists enjoying Rome in the spring, and thousands of pilgrims who had planned to attend the Sunday canonisation of Carlo Acutis, which was postponed after Francis died.

But there has been a genuine outpouring of emotion following the death of a pope who sought to steer the Church towards a more inclusive direction during his 12-year-long papacy.

Maria Mrula, 28, a student from Germany, said she drove 16 hours to be at the funeral.

By "giving to the poor and being with the poor", Francis had inspired many, she said.

"The Church is alive," she said. "It was great being here."

Italian and Vatican authorities mounted a major security operation for the ceremony, with fighter jets on standby and snipers positioned on roofs surrounding the tiny city state.

Red-robed cardinals and purple-hatted bishops sat on one side of the altar in St Peter's Square during the funeral, with world dignitaries sitting opposite.

In front of the altar lay the pope's simple cypress coffin, inlaid with a pale cross.

- 'Bridges not walls' -

The funeral set off nine days of official Vatican mourning for Francis, who took over following the resignation of Pope Benedict XVI in 2013.

After the mourning, cardinals aged under 80 will elect a new pope from among their number.

Many of Francis's reforms angered traditionalists, while his criticism of injustices, from the treatment of migrants to the damage wrought by global warming, riled many world leaders.

Yet the former archbishop of Buenos Aires's compassion and charisma earned him global affection and respect.

"His gestures and exhortations in favour of refugees and displaced persons are countless," Battista Re said.

He recalled the first trip of Francis's papacy to Lampedusa, an Italian island that has become the initial port of call for many migrants crossing the Mediterranean, as well as when the Argentine celebrated mass on the border between Mexico and the United States.

Trump's administration drew the pontiff's ire for its mass deportation of migrants, but the president has paid tribute to "a good man" who "loved the world".

Making the first foreign trip of his second term, Trump had what the White House called a "very productive" meeting with Zelensky before the funeral, before flying out shortly after.

Kyiv published a photo of the encounter, the two men sitting face to face in red and gold chairs in the basilica as the pope's coffin lay nearby, out of shot.

In the homily, Battista Re highlighted Francis's incessant calls for peace, and said he had urged "reason and honest negotiation" in efforts to end conflicts raging around the world.

"'Build bridges, not walls' was an exhortation he repeated many times," the cardinal said.

Trump's predecessor, Joe Biden also attended the funeral, alongside UN Secretary-General Antonio Guterres, Germany's Olaf Scholz, Italy's Giorgia Meloni, and Lebanon's Joseph Aoun.

Israel -- angered by Francis's criticism of the war in Gaza -- sent only its Holy See ambassador. China, which does not have formal relations with the Vatican, did not send any representatives.

- 'Brought them together' -

Italian mourner Francesco Morello, 58, said the homily about peace was a "fitting, strong and beautiful message".

Of the world leaders gathered, Morello noted: "He could not bring them together in life but he managed it in death."

Francis died of a stroke and heart failure less than a month after he left the hospital where he had battled pneumonia for five weeks.

The Church's 266th pope loved nothing more than being among his flock.

His last public act, the day before his death, was an Easter Sunday blessing to the world, ending his papacy as he had begun it -- with an appeal to protect the "vulnerable, the marginalised and migrants".

The Jesuit chose to be named after Saint Francis of Assisi, saying he wanted "a poor Church for the poor". He lived at a Vatican guesthouse rather than the papal palace.

Catholics around the world held events to watch the proceedings live, including in Buenos Aires, where Francis was born as Jorge Bergoglio in the poor neighbourhood of Flores in 1936.

"The pope showed us that there was another way to live the faith," said Lara Amado, 25, in the Argentine capital.

- Refused to judge -

Francis's admirers credit him with transforming perceptions of the Church and helping revive the faith following decades of clerical sex abuse scandals.

He was considered a radical by some for allowing divorced and remarried believers to receive communion, approving the baptism of transgender believers and blessings for same-sex couples, and refusing to judge gay Catholics.

But he also stuck with some centuries-old dogma, notably holding firm on the Church's opposition to abortion.

Francis strove for "a Church determined to take care of the problems of people and the great anxieties that tear the contemporary world apart", Battista Re said.

"A Church capable of bending down to every person, regardless of their beliefs or condition, and healing their wounds".