The former leader of the mainly Catholic Social Democratic and Labour Party (SDLP) helped forge the 1998 Good Friday peace agreement in the British province after a conflict that left 3,500 people dead.
"John was a husband, a father, a grandfather, a great-grandfather and a brother".
As the province's peace process began to progress in the 1990s with several ceasefires by the Irish Republic Army (IRA) paramilitary group, Hume worked to engage U.S. politicians, notably Bill Clinton.
"John Hume genuinely was a political titan", Blair said.
Meanwhile, SDLP Leader Colum Eastwood hit out at those responsible for a number of hijackings in Derry just hours before Mr Hume's remains arrived at St Eugene's.
"He saw the power of political leadership to bring a divided people together around a common goal, without which the Good Friday Agreement would never have come to pass".
Galway West TD Eamon O'Cuiv told Keith Finnegan on Galway talks John Hume did a lot for the country - often against the odds....
"I think people in Ireland will remember John - people north and south, and people around the world who value peace - will remember John Hume for centuries to come", added Mr Mitchell. In the days ahead, Ireland will be united in mourning his loss.
Many Americans who care deeply about Northern Ireland would mourn the passing of the late SDLP leader and the contribution he made to strengthening transatlantic relations, added Mr Pompeo.
"The heartfelt and honest condolences that we have received from people across the island, but particularly from the communities John loved being a part of, have been immensely comforting to us".
He sought self-government for Northern Ireland with power divided among the groups forming it.
Tributes poured in for Hume from across the political spectrum.
Then in 1998, his efforts of over 30 years paved the way for the signing of the Good Friday Agreement.
Born on January 18, 1937, in Northern Ireland's second city - Londonderry to British Unionists, Derry to Irish nationalists - Hume trained for the priesthood before becoming a fixture on Northern Ireland's political landscape.
Local woman Roisin Doherty was typical of many residents when she said she was greatly saddened at the lack of opportunity to pay respect to Mr Hume.
"While the 1998 Good Friday Agreement was the product of many people's work, can anyone really claim that it would have happened without John Hume?".
Taoiseach Micheál Martin said it was "impossible" to express the significance of Hume's life as one of the "towering figures" of Irish public life. We also owe it to him to ensure that the peace he pursued so resolutely is maintained and strengthened.