British and Irish officials will maintain contact with republicans and the other main parties over the weekend to establish if there is any remaining prospect of breaking the political deadlock.
Renewed efforts by the two governments to get agreement enabling publication of their blueprint for the restoration of devolution are expected next week.
The president of Sinn Féin, Mr Gerry Adams, said yesterday that work to find a way through the current deadlock over Mr Tony Blair's demand for "acts of completion" would continue.
"We are not giving up," Mr Gerry Adams said. "Sinn Féin is in this to the end."
Based on ongoing contact with the parties, the two governments will make one more determined effort next week to try to persuade the IRA to provide a new statement making clear that it is ceasing all paramilitary activity, according to officials from the two governments.
Sources in Dublin said the two governments were likely to decide soon whether to maintain the momentum or to "park" the process for a number of months, as suggested on Thursday by the Minister for Justice, Mr McDowell.
Although officials are striving for a breakthrough, the mood is still more pessimistic than optimistic, British and Irish sources have conceded.
Both governments insist that the Assembly elections on May 29th will proceed, even though this could be devastating for Mr David Trimble's leadership of the Ulster Unionist Party, and for the pro-Belfast Agreement wing of unionism.
Mr Trimble said the process was being held up by "a couple of hundred hoods". "What we've got is a couple of hundred people who don't want to give up the old ways and who still benefit from the old ways, particularly in terms of racketeering. If we see it as being just the problem of a couple of hundred hoods I think we see the way forward more clearly.
"What is being asked for isn't anything new. It is what the agreement said - the complete disarmament of paramilitary groups and operating purely peacefully without a private army. Republicans have singularly failed to deliver on these matters."
Mr Trimble was speaking in the wake of Mr Adams's speech in Newry, Co Down, on Thursday night in which the Sinn Féin leader claimed the IRA's statement to the two governments was "clear and unambiguous".
He told a party rally: "It contains a number of highly significant and positive elements unparalleled in any previous statement by the IRA leadership."
Mr Trimble made it clear he was not calling for another postponement of Assembly elections, but he did warn about the consequences of holding them in a climate of political uncertainty. "Simply to sleepwalk into an election without telling people what we're going to do would be wrong," he cautioned.
"I know that time is short because the \ government has spent a lot of time trying to get republicans to carry out their obligations and have failed to do that. There isn't, at present, a need to postpone the elections. But if the question is not addressed satisfactorily then the government have to do some hard thinking." Speaking on the Falls Road on Belfast, Mr Adams said: "Everybody needs to remember there is a collective responsibility in this and all of the main parties and the two governments need to be reflective and contemplative of how far we have come. They have to be mindful that this is a process and see if we can move forward to get the next bit of business done."
Dublin and London hope that this weekend those "who have been immersed to the point of exhaustion in these negotiations" can step back from the talks to recover some energy.
"People need to come up for air," said one Irish insider.
If next week's attempt fails, then Mr Ahern and Mr Blair will put things on hold until the autumn, said British and Irish sources.