A package to fund the transfer of policing and justice powers from Westminster was brokered in late night talks in London.
But while Sinn Féin said British Prime Minister Gordon Brown had effectively concluded crucial discussions on financing the plan, DUP leader Peter Robinson said he would not be rushed into an early deal.
Now Mr Brown is to provide written confirmation of his financial blueprint to the parties on Monday, a move which will coincide with the arrival of a top level US delegation to Belfast, led by US Secretary of State Hillary Clinton.
Northern Ireland Deputy First Minister Martin McGuinness emerged from four hours of talks at Number 10 at around midnight and said major progress had been made.
'What I believe now is that we can be very pleased at the outcome that we have had tonight,' he said.
'I think that from our perspective we have now arrived at the point where we can say with some considerable confidence that we have brought these discussions to a successful conclusion.'
The senior Sinn Féin representative said major progress had been made towards agreeing the final devolution of the powers.
'I am pleased, I think that represents a real achievement on our part, on my part, on Peter's part, on the efforts made by Gordon Brown and indeed others.'
The devolution of policing and justice was promised in the St Andrews agreement that paved the way for setting-up the power-sharing government in Northern Ireland.
But while republicans have pressed for swift progress on the issue, the DUP has said it wants to make sure key issues, including the financing of the move, are agreed first.
The unionist party also faces a threat from hard-liners who are totally opposed to sharing responsibility for the justice system with Sinn Féin.
The DUP and Sinn Féin last year agreed a series of choreographed moves that would lead to the eventual devolution of the powers.
