Mourners heard that the former SDLP leader put everybody first and did not focus on difference and division.
His funeral service took place at St Eugene’s Cathedral in Londonderry.
“He focused on unity and peace, and giving that dignity to every person,” Father Paul Farren said.
“We should never underestimate how difficult it was for John to cross the road and do what was intensely unpopular for the greater good.
“Even in the darkest moments, when people would have been forgiven for having no hope, John made peace visible for others.
“His vision revealed what could be, and with time and determination and single-mindedness and stubbornness he convinced others that peace could be a reality.
“He never lost faith in peace and he never lost faith in his ability to convince others that peace was the only way.
“If ever you want to see a man who gave his life for his country, and his health, that man is John Hume. The world knows it.”
Mr Hume’s son John Hume Junior said that his dad made them “laugh, dream, think”.
He told mourners that he was a Derryman to his core.
Mr Hume added: “If dad were here today, in the fullness of his health, witnessing the current tensions in the world, he wouldn’t waste the opportunity to say a few words.
“He’d talk about our common humanity, the need to respect diversity and difference, to protect and deepen democracy, to value education, and to place non-violence at the absolute centre.
“He might also stress the right to a living wage and a roof over your head, to decent healthcare and education.”
Messages were read from former US president Bill Clinton, Prime Minister Boris Johnson and U2 singer Bono.
Among those attending the requiem mass includes Ireland’s President Michael D Higgins, Taoiseach Micheal Martin, First Minister Arlene Foster and Deputy First Minister Michelle O’Neill.
Others included former SDLP leader Mark Durkan and current leader Colum Eastwood.
Derry musician Phil Coulter, who is expected to play The Town I Loved So Well at the end of the service, is also attending the mass.
Pope Francis also paid tribute to Mr Hume.
A statement from the Vatican said: “His Holiness Pope Francis was saddened to learn of the death of John Hume, and sends the assurance of his prayers to his family and to all who mourn his loss.
“Mindful of the Christian faith that inspired John Hume’s untiring efforts to promote dialogue, reconciliation and peace among the people of Northern Ireland, his Holiness commends his noble soul to the loving mercy of Almighty God.”
A message from the Dalai Lama was also read during the service.
“I was pleased to be able to meet John during one of my several visits to Northern Ireland,” he said.
“Indeed, his deep conviction in the power of dialogue and negotiations in resolving the problem in his homeland has been an example of non-violent resolution of issues.
“It was his leadership and his faith in the power of negotiations that enabled the 1998 Good Friday Agreement to be reached. His steady persistence set an example for all of us to follow.
“Although my fellow Nobel laureate is no longer with us, his message about peace and non-violence in the resolution of conflict, no matter how protracted or difficult it may seem to be, will long survive him. He lived a truly meaningful life.”
The Derry politician, feted around the world as a peacemaker, died on Monday at the age of 83 after a long battle with dementia.
In ordinary circumstances, Mr Hume’s funeral would have been expected to draw huge crowds, but numbers are limited due to coronavirus restrictions.
Mr Higgins, Mr Martin, Prime Mr Johnson and Northern Ireland Secretary Brandon Lewis all lit flames for the SDLP founding member.
Mr Hume was a key architect of the Good Friday Agreement and was awarded the Nobel prize for the pivotal role he played in ending the region’s sectarian conflict.
The former MP, Stormont Assembly member and MEP, led the party he helped found for 22 years.
He was a prominent figure in the civil rights campaigns of the late 1960s and also played a leading role in the formation of the credit union movement.
Throughout his political career, he remained steadfast in his commitment to non-violence.
His participation in secret talks with then Sinn Fein president Gerry Adams in the late 1980s and early 1990s was a key catalyst for the nascent peace process.
The SDLP leader faced intense criticism, including some from within his own party, when his dialogue with Mr Adams became public in 1993.
Despite threats to his life, he persisted with his efforts to engage with the republican movement and to convince the IRA to end its campaign of violence.
The highlight of Mr Hume’s career came in 1998 with the signing of the historic Good Friday accord which largely ended Northern Ireland’s 30-year sectarian conflict.
Along with Ulster Unionist Party leader David Trimble, now Lord Trimble, Mr Hume was awarded the Nobel peace prize for his contribution to stopping the bloodshed.
In 2010, Mr Hume was named “Ireland’s Greatest” in a poll by Ireland’s national broadcaster RTE.
His death came just six months after that of fellow Good Friday architect and long-time SDLP deputy leader Seamus Mallon.
A number of vehicles were hijacked in Derry on Tuesday afternoon, with SDLP leader Colum Eastwood accusing those responsible of violating the grief of the city.