There is growing hope that the DUP and Sinn Fein are on the verge of signing a deal on the transfer of policing and justice powers to Northern Ireland.
The difficulty in reaching a deal had raised doubts over the future of the power-sharing assembly. Talks aimed at finalising an agreement will resume at Hillsborough Castle this morning.
Martin McGuinness, Sinn Fein's deputy First Minister, said: "I am happy to say we have made significant progress. Institutions which don't deliver are worthless and something I will not be involved in.
"I now hope we have a basis upon which nationalists, republicans, unionists and loyalists will move forward together on the basis of partnership and equality. There is no other realistic or viable path available."
DUP MP Gregory Campbell said the public should be consulted on any agreement.
"People need to be consulted, they need to see the bones of the deal and the detail of it, and then give a response that allows us to say whether we proceed or don't," he said.
Gordon Brown and the Irish prime minister Brian Cowen may return to Northern Ireland later on Monday, if a deal is finalised.