The NI Assembly has held a special session to remember its former deputy first minister Martin McGuinness.
The Sinn Féin politician died early on Tuesday in a Londonderry hospital with his family by his side. He was 66 years old.
He had been suffering from a rare heart condition. His funeral is to take place in his native Derry on Thursday.
Speaking at PMQs in Westminster, Theresa May said people should not “condone or justify the path he took in the earlier part of his life and we should never forget the victims of terrorism”.
She supported remarks made on Tuesday by former UUP leader Lord Trimble who said Mr McGuinness played an indispensible role in bringing the “republican movement away from violence” and “building a better Northern Ireland”.
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At Stormont, meanwhile, Sinn Féin’s northern leader Michelle O’Neill described Mr McGuinness as a “political visionary”.
DUP leader Arlene Foster said while “many victims are feeling very hurt”, she acknowledged that many republicans were mourning “a leader, a friend, or a mentor”.
SDLP leader Colum Eastwood said Mr McGuinness’ “journey” began in violence but ended “grounded in the principles of peace and partnership”.
Outgoing UUP leader Mike Nesbitt said he was “clearly a man of his word, a straight-dealing individual, and he was a man of political integrity”.
Alliance Party leader Naomi Long told the Assembly she did not believe there would be peace in Northern Ireland had it not been for people like Martin McGuinness.
But TUV leader Jim Allister said his thoughts were with the families of IRA victims.
“His hands drip with the blood of the innocent,” said Mr Allister of Martin McGuinness.
The flag above Leinster House (Irish parliament) in Dublin will be flown at half-mast on Thursday.
BBC News NI’s Political Editor Mark Devenport
The negotiations to restore Stormont’s power-sharing executive have a 27 March deadline.
It’s undoubtedly the case that his funeral will mean that the time that the Northern Ireland Office thought that they had to continue negotiating before the deadline will be taken up with other matters.
What impact will this have on the chances of agreement? They seemed pretty slim prior to Martin McGuinness’ death.
They still, I think, seem fairly slim although maybe it will inject a new mood into some of the discussions.
Vigils were held in Derry, Belfast and Dublin for the republican figurehead, who worked at the heart of the power-sharing government following the 1998 Good Friday Agreement.
A book of condolence has been opened in a number of places, including Belfast City Hall.
Mr McGuinness became deputy first minister in 2007, standing alongside Democratic Unionist Party leaders Ian Paisley, Peter Robinson and Arlene Foster.
A visibly ailing Mr McGuinness stood down from his post in January to protest against the DUP’s handling of an energy scandal, in a move that triggered a snap election.
Analysis: BBC News NI Home Affairs Correspondent Vincent Kearney
No-one knows how many people Martin McGuinness killed, directly or indirectly.
As a senior commander in the Provisional IRA for many years, there is no doubt there was blood on his hands.
Security sources say he went on to become chief of staff of the organisation from the early 1980s, right through until the end of the IRA’s campaign of violence.
Nothing happened in Derry without him knowing.
Sinn Féin president Gerry Adams said: “He was a passionate republican who worked tirelessly for peace and reconciliation and for the re-unification of his country. But above all he loved his family and the people of Derry and he was immensely proud of both.”
Those who lost loved ones, or were injured in the IRA’s bombing campaigns, harbour painful memories.
Some said the pain had been soothed by McGuinness’ willingness to compromise for peace in Northern Ireland. Others were less forgiving.
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Martin McGuinness grew up in Derry’s Bogside, radicalised, he said, by discrimination and murder in his city.
In 1972, at the age of 21, he was second-in-command of the IRA in Derry at the time of Bloody Sunday, when 14 civil rights protesters were killed in the city by soldiers.
The years that followed saw the IRA hunger strikes, the Brighton bombing when Margaret Thatcher and the Tory Party conference were targeted and the Enniskillen bomb in 1987, in which 11 people died.
His shift to politics came slowly. Martin McGuinness was chief negotiator in the blossoming peace process and took on the post of education minister.
By 2007, he was Northern Ireland’s deputy first minister.
In recent years, he said: “My war is over. My job as a political leader is to prevent that war and I feel very passionate about it.”
Mr McGuinness’ funeral will leave his home on Thursday at 13:20 GMT ahead of Requiem Mass at St Columba’s Church Longtower at 14:00. He will be buried in the City Cemetery.
Martin McGuinness: NI Assembly remembers former minister}