The family of John Hume have said the "heartfelt and sincere condolences" they have received have been "immensely comforting".
They had asked people to "light a candle for peace" tonight and to adhere to Covid-19 guidelines ahead of his funeral tomorrow.
The former SDLP leader and Nobel laureate died yesterday aged 83.
Mr Hume made his final journey home to his native Derry this evening. His body was brought from Moville in Co Donegal 18 miles across the border to St Eugene's Cathedral in the city ahead of his funeral tomorrow.
A socially distanced guard of honour made up of party activists watched on as the procession made its way to the doors of the cathedral.
They held candles in memory of the man feted around the world as a peacemaker, in line with the family's wishes.
Mr Hume worked tirelessly to bring an end to the violence in Northern Ireland, reaching out both to paramilitaries and politicians.
In 1998, he and then UUP leader David Trimble were awarded the Nobel Peace Prize.
In ordinary circumstances, Mr Hume's removal service and subsequent funeral would have been expected to draw huge crowds, but numbers will now be limited due to coronavirus restrictions.
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His family asked people, in light of Covid-19 restrictions, that instead of lining roads and streets, they "light a candle for peace in their homes or at their door".
The family said they know that Mr Hume would "have prioritised public health and the safety and health of our communities".
President Michael D Higgins and his wife Sabina lit a candle tonight at Áras an Uachtaráin.
Following a request from John Hume's family, President Higgins and Sabina this evening lit a "candle for peace" at Áras an Uachtaráin. pic.twitter.com/3GPZhkfRkp— President of Ireland (@PresidentIRL) August 4, 2020
Tonight we join together to light a candle for peace and reflect on the huge contribution John Hume made to our society. He brought people together and secured peace on this island. He truly was "Ireland's Greatest". Thank you John #JohnsLight pic.twitter.com/Y19HAxsGtB— Micheál Martin (@MichealMartinTD) August 4, 2020
British Prime Minister Boris Johnson also lit a candle at Downing Street.
Tonight a candle has been lit in memory of John Hume and placed in the door of Downing Street. A symbol to all of us of the peace he was so instrumental in securing, and a reminder of the long-lasting impact he had on the world. #JohnsLight pic.twitter.com/jby5TZQYER— Boris Johnson (@BorisJohnson) August 4, 2020
A politician blessed with all the gifts
Tributes paid to 'great hero and true peacemaker'
From the archives: A profile of John Hume
In pictures: John Hume, a life in politics
Mr Hume was one of a number of Stormont MPs who founded the Social Democratic and Labour Party in 1970.
In 1979, he was elected to the European Parliament as an MEP for Foyle, a role he held until 2004. He also served as MP for Foyle in Westminster from 1983 to 2005.
In 2001, Mr Hume resigned as leader of the SDLP, citing ill health. He gave up his seat in Brussels in 2004 and at Westminster in 2005.
Online books of condolence have been opened by local authorities including Derry City and Strabane District Council, Dublin City Council, Cork City Council, Wicklow County Council and Kerry County Council.
Bishop of Derry Donal McKeown said there was a sense of real sadness and also pride in the city of Derry, as news of Mr Hume's death filtered through the community.
He said Mr Hume never lost his roots because he was "not committed to the party, nor to any idealogy", but to making a better future for the city.
Bishop McKeown said Mr Hume's funeral will be a family one in adherence to Covid-19 restrictions, and while it will obviously be sad, he added, it will be one with an element of gratitude for the wonderful human being that he was.
Mr Hume's funeral mass at 11.30am tomorrow will be broadcast on RTÉ One Television and on RTÉ News Now, and streamed on the RTÉ News website.