The Taoiseach Mr Ahern said this afternoon that progress was made after 34 hours of talks at Leeds Castle ended without final agreement but admitted "it was not possible ... to secure total agreement on the institutional issues".
"Our hope is that it will be possible to close that loop and thereby secure a fully comprehensive agreement providing for the restoration of the Northern Ireland assembly and the executive. However, quite frankly it is only the parties themselves who can agree to changes to the institutions."
A new round of talks planned between the Northern Irish Secretary, Mr Murphy and the Minister for Foreign Affairs, Mr Cowen, at Stormont, possibly as early as next week. Early indications are that the deal stalled because the DUP attempted to make changes to the Belfast Agreement.
British Prime Minister Mr Tony Blair
Despite failing to agree a deal, both leaders believe that significant progress has been made on persuading the IRA to disarm and effectively wind itself up.
Mr Ahern claimed the talks had set up the chance to secure the acts of completion on decommissioning, troop reductions and the transfer of policing powers from Westminster to Belfast.
He said: "It's absolutely vital that we do not falter at the last hurdle. "I urge all the parties and particularly those in positions of power and responsibility to finish the job in the interests of all the people in Northern Ireland."
His optimism on a possible resolution to the arms issue was echoed by the British Prime Minister Mr Blair who said: "We believe we can resolve the issues to do with ending paramilitary activity and putting weapons beyond use".
Mr Blair said even though no IRA statement was given he was confident that the weapons issue which had dogged the peace process has been resolved. The deadlock was over how the political institutions at Stormont would function.
"There is, however, not yet comprehensive agreement on how to change the strands one, two and three of the Good Friday Agreement without damaging the fundamentals and the fair and inclusive basis of the agreement," he said.
The Taoiseach Mr Ahern with the British Prime Minister Tony Blair during a press conference
"The issue of ending the violence as a result of what we discussed and the outline of what we have got here, I think that can be done. "I can't believe myself that this set of institutional issues is going then to scupper what otherwise would be a very good deal."
"For us this is the end of the detailed negotiation. We're not coming back in and doing another great detailed negotiation because everyone knows where we stand on the issues and the parties know that very well," Mr Blair added.
Mr Ahern said that for the last two years talks have centred on acts of completion to deal with the arms issue and also policing.
Mr Ahern added it was never the case that the power-sharing institutions would have been up next week even if a deal was agreed.
Sinn Fein President Mr Gerry Adams said there had been an effort to get a comprehensive agreement but he was unequivocal about why this had not been possible.
The problem was "essentially about elements of political unionism and their failure or reticence to embrace a process of change".
"One party did not negotiate, one party did not talk to the rest of us, so therein you have some sense of where all of this is."
The DUP leader Mr Ian Paisley saw things differently and said a "golden opportunity" had been made available to realise a stable and entirely peaceful future for the province.
"We have never been closer to solving the problems that have plagued us for decades," he said.
"The decommissioning of IRA weapons and dismantling of the structures of terrorism is the ultimate outcome of the discussions."
The SDLP leader Mr Mark Durkan said the parties intended to continue with negotiations next week. "Progress has been made, positive but not conclusive, there are still issues that are outstanding," he said.
The sense of progress being made was reinforced by the UUP leader Mr David Trimble who said there was disappointment that a deal had not been reached, as "significant progress" had been made.
Agencies