Shadow chancellor John McDonnell has apologised "from the bottom of my heart" for the offence caused by calling for Irish republican terrorists to be honoured but suggested his comments may have helped the peace process.
The senior Labour MP, appointed by Jeremy Corbyn to lead the party's economic policy, said it had been a "mistake" to use the words and accepted he had "clearly" caused offence.
David Cameron said Mr McDonnell should be "ashamed" of the comments when the issue was raised during Mr Corbyn's first session of Prime Minister's Questions as opposition leader.
The row follows Mr McDonnell's remarks in 2003 that "the bombs and bullets and sacrifice" of the IRA had brought Britain to the negotiating table.
Challenged about the comments on BBC1's Question Time Mr McDonnell said: "I accept it was a mistake to use those words, but actually if it contributed towards saving one life, or preventing someone else being maimed, it was worth doing because we did hold onto the peace process.
"There was a real risk of the republican movement splitting, and some continuing with the armed process. If I gave offence, and I clearly have, from the bottom of my heart I apologise."
In 2003 Mr McDonnell told a meeting in London: "It's about time we started honouring those people involved in the armed struggle. It was the bombs and bullets and sacrifice made by the likes of (hunger striker) Bobby Sands that brought Britain to the negotiating table.
"The peace we have now is due to the action of the IRA."
In the Commons on Wednesday, the Prime Minister joined the DUP leader Nigel Dodds in condemning the remarks.
Mr Cameron said: "I have a simple view which is the terrorism we faced was wrong, it was unjustifiable, the death and the killing was wrong. It was never justified and people who seek to justify it should be ashamed of themselves."
The shadow chancellor used his Question Time appearance to also apologise for an "appalling joke" in 2010 about wanting to assassinate Margaret Thatcher.
"It was an appalling joke. It's ended my career in stand-up, let's put it that way, and I apologise for it as well."
The shadow chancellor said Labour favoured a return to the "reasonable" 50p top rate of income tax, playing down suggestions that he and Mr Corbyn could push for it to rise to as much as 70p.
He also insisted that Labour was not advocating withdrawal from the Nato alliance.