The Northern Secretary has said she believed the war was over for the IRA and other paramilitary groups currently maintaining what she described as "unequivocal ceasefires".
But the Sinn Fein president, Mr Gerry Adams, yesterday detailed the conditions necessary before republicans could say that the war was over.
Earlier a spokesman for the Progressive Unionist Party, Mr David Ervine, again demanded a declaration from the republican leadership that the war was over, which he said was necessary to reassure unionists and to save the Belfast Agreement. He said he had been seeking this declaration privately for some time, and was now calling for it publicly.
Dr Mo Mowlam said she accepted the good faith of those parties at the talks linked to paramilitary organisations. "I think the war is certainly over for groups that have signed up to an unequivocal ceasefire, and their political representatives are in the talks process. I have accepted that they are acting in good faith and the security advice I get supports that."
In determining which prisoners were eligible to apply for early release under the terms of the agreement, the British government accepted that the IRA, the UVF and the UDA/UFF were maintaining unequivocal ceasefires, she said.
Dr Mowlam said the war was certainly not over for splinter groups, which were trying to destroy the prospects for peace and bring down the agreement.
She agreed with Mr Ervine that Sinn Fein had to take "further steps forward", but said every other party to the talks process had to do so also.
Mr Adams said that bringing an end to war "requires more than words or word games about whether the war is over".
In an article in yesterday's Irish News, he added: "It demands action, consistent and continuous, until we have a democratic peace settlement." Mr Adams accused unionists of demanding a formula of words, which was yet another precondition.
Sinn Fein was working for an end to war in Ireland. He was conscious of the difficulties unionists faced "in participating in a process of change" and engaging with those they saw as enemies. The Sinn Fein leader urged unionists to stop making excuses and to start talking.
Mr Adams said: "The war will be over when all of those who have engaged in war - and some are still engaging in war - stop; when the British army of occupation, which still maintains a huge military presence in republican areas, begins demilitarising instead of remilitarising; when all of the prisoners are free; when there is justice and equality and when we have a proper policing service.
The Sinn Fein president added: "When all of these matters have been tackled and resolved and when we have a democratic peace settlement, then we will, with some sense of certainty, be able to say that conflict is now part of our past - that the war is over."
Mr Adams said Sinn Fein was "totally wedded to democratic and peaceful means of advancing our political objectives", and that the party had demonstrated good faith "by taking an entire constituency of republican activists into a totally new phase, which I think the people of this island recognise has the potential to bring about a peace settlement".
Mr Adam's comments were interpreted in some quarters as an indication that the war was not yet over as far as republicans were concerned. The front-page headline in the Belfast Telegraph read: Adams: `war is not over'.
Mr Martin McGuinness said yesterday that Sinn Fein "was not at war with anyone" adding: "We have used our influence to create the conditions we now have. I believe that the IRA, of all the armed groups, has been the most disciplined."