Jeremy Corbyn has condemned "all acts of violence from wherever they came" during the Troubles in the North, but declined to specifically denounce the IRA as terrorists.
The UK Labour leader spoke after Northern Ireland Secretary James Brokenshire accused him of having "IRA sympathies" and urged him to make clear whether he believes the group were terrorists and if their actions should be "unequivocally" condemned.
Mr Corbyn has come under fire for refusing to single out the IRA for condemnation when pressed over his past campaigning activities, and he again refused to mention them specifically.
Mr Brokenshire's questions were put to Mr Corbyn by a reporter after the Labour leader gave a speech in Hull.
Mr Corbyn said: "I condemn all acts of violence in Northern Ireland from wherever they came.
"I spent the whole of the 1980s representing a constituency with a large number of Irish people in it, we wanted peace, we wanted justice, we wanted a solution.
"The ceasefire, the first ceasefire, helped to bring that about, and bring about those talks, which were representative of all sections of opinion in Northern Ireland."
The Labour government after 1997 helped to bring in the historic Good Friday Agreement, the basis of which was the recognition of the differing cultural histories and values of the North, and it stood the test of time and it's still there, he added.
"We have devolved administration in Northern Ireland and I think we should recognise that that peace was achieved by a lot of bravery, both in the unionist community as well as in the nationalist community - people that walked a very difficult extra mile when they were under pressure from their communities not to do so - both republicans and unionists walked that extra mile and brought us the Good Friday Agreement.
"And I think we should use this election as thanking those that brought about the Good Friday Agreement."
Mr Corbyn and shadow chancellor John McDonnell have faced scrutiny over their association with Irish republicans.
Before the IRA ceasefire, they controversially met Sinn Fein a number of times in Westminster during the 1990s.
The row over the pair's past activities has prompted the intervention of Gerry Adams and Bertie Ahern, both highly significant figures in the era.
Sinn Fein president Mr Adams said Mr Corbyn was "on the right side of history" in supporting Irish republicans and had respected the party's democratic mandate.
"What he did was very modest, what he did was very fundamental," Mr Adams said.
Former Taoiseach Mr Ahern, who worked with former prime minister Tony Blair and Northern politicians to secure the 1998 Good Friday Agreement - which largely ended 30 years of trouble in the North - warned against digging up "any of the enmities, animosities of the past".
The retired Dublin politician told ITV's Good Morning Britain programme: "Of course we all condemn the violence of all sides in the past and we want to move on.
"Jeremy Corbyn, I think, always kept the door open to Sinn Fein during those difficult days, but we want to get away from the violence of the past and hopefully that never returns."
Mr McDonnell has apologised for comments he made praising the IRA's "bravery" in 2003.
After becoming Labour leader in 2015, Mr Corbyn defended reaching out to republicans during the Troubles - insisting he wanted the violence to stop.
But Mr Brokenshire said: "I have listened with interest and concern to the various attempts by Jeremy Corbyn and John McDonnell to explain their attitudes towards IRA terrorism during the 1980s and 1990s.
"Their complete failure unequivocally to condemn terrorism, and to attempt to contextualise it, are deeply worrying coming from two people who in just over two weeks seek to be entrusted with the security of the United Kingdom."
Democratic Unionist leader Arlene Foster said Mr Corbyn's refusal to denounce the IRA as terrorists was "abhorrent" .
Northern Ireland's former first minister told a meeting of the Bruges Group in central London: "Here we have a man who is putting himself forward to lead our nation and yet he cannot condemn an organisation which was taking away the fundamental human rights of British citizens living not just in Northern Ireland but right across the United Kingdom.
"I think he has put himself outside the political pale - I think it is abhorrent he seems to be caught up with the perpetrators of violence without any thought for those of us who were victims of the IRA violence through the Troubles."
Ms Foster said she "absolutely" wants Mr Corbyn to condemn the IRA as an organisation, adding: "It is wrong and he should say it is such, but instead he has advocated on behalf of the IRA, he has put forward petitions for some of their members, he has attended memorial services for those who he calls brave people - who I would call terrorists - so I'm sorry there will be no meeting of minds between myself and Jeremy Corbyn."
Ms Foster also claimed that Mr Corbyn "wanted the IRA to win".
She said: "It's not just that he reached out to the IRA and spoke to them - there are many fine people who tried to speak to the IRA to ask them to desist and stop what they were doing.
"He actually supported them - he wanted the IRA to win.
"That's the fundamental difference between those who reached out to all sides during the Troubles - he didn't do that and I think it should be called out for what it is."
Security minister Ben Wallace, who served in the North as a soldier during the Troubles, said: "It is a disgrace that a man who wants to be prime minister cannot describe the IRA as terrorists, and to suggest otherwise is an insult to the victims and relatives whose lives were devastated by the IRA's murderous campaign of violence.
"Anyone who has ever experienced the fear and horrendous aftermath of indiscriminate bombings and shootings will know that the IRA were ruthless terrorists.
"Anyone who has had to experience the horror of picking pieces of bodies off the streets, or had to bury a loved one after one of their attacks will know that Mr Corbyn is dangerously deluded and morally bankrupt.
"No ifs, no buts, the IRA were terrorists who murdered hundreds of people and ruined thousands more lives.
"If Jeremy Corbyn cannot say that then he is unfit to be prime minister."