The British and Irish Governments said they were optimistic that a crisis can be avoided in the Northern Ireland political process.
They called for the devolution of policing and justice powers to the region "at an early date".
Prime Minister Gordon Brown and Taoiseach Brian Cowen held talks at Downing Street last night after fears that the future of the Stormont power-sharing government could be threatened.
Sinn Fein and the Democratic Unionist Party (DUP) are split over when the policing powers should be devolved, and republicans have said crisis can only be averted if a deal is agreed by Christmas.
The governments announced plans last night for fresh talks with the parties over the "next few weeks", and despite fears in Belfast of a political collapse of the Stormont regime and early Assembly elections, Mr Brown said he remained optimistic.
During a break in the inter-governmental talks, the Prime Minister said his discussions with Mr Cowen had been good.
Mr Brown said: "It is partly because of that that I am optimistic about the way forward.
"I know that there are still challenges to be met... but I do say that I am confident that both sides see a way forward."
The Prime Minister said a "lot of progress" had been made, but he was careful not to set a deadline on the way forward.
Mr Cowen said he also believed the parties could "build on the progress" that had been achieved.
"The people of Northern Ireland have been through a lot over the years, as we know," he said. "They want this to work."
Sinn Fein has said it entered government with the DUP in 2007, and changed republican policy to support the new police structures in Northern Ireland, on condition that political responsibility for policing was devolved from Westminster to the Assembly.
Republicans accuse the DUP of failing to support agreements on the timing of the move, claiming the DUP leadership is under pressure from hardliners.
Sinn Fein has demanded a deal by Christmas, but the DUP has said it will not be pressed into a quick agreement, insisting it has conditions that must first be met.
A joint statement issued by the two governments when last night's talks ended called for the full implementation of the political agreements that underpin power-sharing.
It said: "In this regard, the Prime Minister and the Taoiseach stressed the importance of the early completion of the devolution of justice and policing powers, now that the enabling financial package was in place.
"They agreed that this was necessary both to consolidate the functioning of the devolved institutions and to complete the transformation of policing in Northern Ireland."
Both premiers said the police on both sides of the Irish border were successfully tackling dissident republican groups opposed to the peace process.
They said: "The Prime Minister and Taoiseach agreed to work closely together, and with the parties, in the next few weeks to overcome the remaining obstacles to finding an agreed basis on which the devolution of justice and policing powers can take place at an early date."
The DUP has said it will not agree to a quick deal in the face of Sinn Fein demands, and has called for confidence-building measures for unionists ahead of agreement.
The British Government has already tabled a £1 billion package to fund the transfer of the powers and, together with the Irish Government, has highlighted the many obstacles the peace process has overcome in the past.
The DUP has called on Government to agree to a series of moves before the party supports devolution of policing powers.
Mr Brown has already tabled a £1 billion package to finance the devolution process and offered a further £20 million for former Royal Ulster Constabulary reservists who missed out on earlier compensation around the introduction of the new Police Service of Northern Ireland (PSNI).
The DUP also wants the scrapping of the Parades Commission which rules on controversial Orange Order marches, plus easier access to protection weapons for ex-security force members, and has called for a reprieve for the PSNI full-time reserve which is to be scrapped.
Mr Robinson recently repeated his party's preference for scrapping the power-sharing voting structures at the heart of the Stormont administration.
"In essence, our proposals include the abolition of community designation and its replacement by a 65% weighted majority voting," he said.
Sinn Fein said the proposal amounted to a return to unionist majority rule.