Negotiations aimed at restoring devolved government in Northern Ireland have ended without a deal being reached, Tony Blair has said.
Blair and Ahern are 'determined to move ahead'
However, the British prime minister said he believed the issue of ending paramilitary activity and putting weapons beyond use could be resolved.
Both Mr Blair and his Irish counterpart Bertie Ahern said nothing must upset the "fundamental equilibrium" of the Good Friday Agreement.
The British and Irish governments put forward a paper at the talks on Saturday which they regarded as an "acceptable compromise" to the DUP's demands for changes to the Good Friday Agreement.
It is understood progress had been made on a form of words which would see an end to IRA activity and the completion of decommissioning by Christmas, but the parties had not actually seen a text.
Discussions between the parties are to continue next week, led by Northern Ireland Secretary Paul Murphy and Irish Foreign Minister Brian Cowen.
Speaking at the close of talks at Leeds Castle in Kent, Mr Blair said: "We believe what is now on offer is reasonable in its substance and historic in meaning.
"We are determined to move ahead."
Irish Prime Minister Bertie Ahern said there was a "real prospect of securing acts of completion that we had been seeking over the past three years".
"We have made progress on key issues of paramilitarism, arms decommissioning and policing. We hope to secure a fully comprehensive agreement," he said.
"It is only the parties themselves who can agree changes to the institutions. "
BBC NI political correspondent Gareth Gordon said the sticking point appeared to be DUP demands for changes to the Agreement and the running of Stormont, particularly the issue of accountability of ministers.
"The issues now appear to be not guns, but government, not paramilitarism but politics," he said.
Sinn Fein President Gerry Adams said there had been an effort to get a comprehensive agreement.
But he said 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."
DUP leader Ian Paisley 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."
Leeds Castle in Kent was the picturesque venue for the talks
UUP leader David Trimble said there was disappointment that a deal had not been reached.
However, he said "significant progress" had been made, raising hopes that the weapons and paramilitary issues could be finally resolved.
"We will be exploring whether the parties that have put forward ideas are doing so in a genuine desire to see the arrangements improve or whether they are doing so out of a desire to wreck the arrangements," he said.
SDLP leader Mark Durkan said the political 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.
'Previously rejected calls'
The talks, which began on Thursday, were seen as the most important since the negotiations leading up to the Good Friday Agreement in 1998.
The discussions were aimed at resolving issues surrounding the deadlock over the IRA's continued existence and power-sharing at Stormont.
The British and Irish prime ministers were working to break down differences between the two main participants, Ian Paisley's Democratic Unionists and Sinn Fein led by Gerry Adams.
A meeting also took place on Saturday between the DUP and the Ulster Unionists, at the request of the UUP. The UUP had previously rejected calls for meetings from the DUP.
The agenda at Leeds Castle included issues such as the continued existence of the IRA, decommissioning, policing and undertakings from unionists to make the institutions work.
The political institutions in Northern Ireland were suspended in October 2002 amid allegations of IRA intelligence gathering at the Northern Ireland Office.