Prime Minister Gordon Brown is to remain in Northern Ireland on Wednesday in a bid to end the dispute between Sinn Fein and the Democratic Unionist Party over the devolution of policing and justice powers.
Reports earlier suggested that a compromise deal to resolve contentious parades could hold the key to securing a breakthrough in marathon talks to save the powersharing government.
As the summit chaired by Prime Minister Gordon Brown and Irish Premier Brian Cowen entered its third day, the fate of the Stormont Assembly is thought to hinge on whether the main parties can find an agreed way forward on the thorny issue.
The talks at Hillsborough Castle, Co Down, were dramatically convened by the two premiers on Monday after the long-running row between the Democratic Unionists and Sinn Fein escalated to crisis point.
Republicans threatened serious consequences for the administration if the DUP did not agree to a swift transfer of law and order responsibilities from Westminster, but the main unionist party insisted it would not give the go ahead until there was progress on the parades front.
The party is demanding an end to the Parades Commission, which currently oversees marches in flashpoint areas such as the Garvaghy Road in Portadown, Co Armagh.
Led by the two premiers, all of Northern Ireland's main parties were involved in round-the-clock talks to hammer out a solution. It is understood an agreement could unlock the possibility of a devolution date before the forthcoming general election.
On Tuesday night all the political leaders met face-to-face during a round table meeting chaired by Mr Brown and Mr Cowen.
Afterwards SDLP leader Mark Durkan said progress had been made on the outstanding issues and called for a deal that would promote true partnership in the coalition government, in which his party holds one ministry. "There were a lot of positive words said around the table, a lot of good words," he said.
A spokesman for Gordon Brown reflected the mood of cautious optimism on Wednesday morning, saying: "We continue to believe that there is scope for agreement on the elements that need to be in place to enable the completion of devolution in Northern Ireland."