The Secretary of State James Brokenshire has extended the deadline for Northern Ireland’s two main parties to reach a deal to restore power-sharing.
The DUP and Sinn Féin left Stormont on Monday without reaching an agreement.
However they have made “further progress” in the negotiations, according to the secretary of state.
Mr Brokenshire said they are making “certain additional requests” of the government which need to be considered.
He said because of this progress the decision on whether to introduce legislation to Parliament to enable an executive to be formed should be deferred.
Talks will resume on Tuesday morning.
Northern Ireland has been without a devolved administration since January, after a bitter dispute between the two parties sparked by the handling of a botched green energy scheme.
In spite of several rounds of discussions, a deal to restore devolution has proved elusive, with Sinn Féin’s demand for legislation to give official status to the Irish language seen as the main dividing issue.
Without any resolution in sight, the government has warned it will have no choice but to intervene, increasing the prospect of direct rule being imposed.
The DUP accused Sinn Féin representatives on Monday of “dragging their feet”, and called on Westminster to press ahead with its budget plan in order to ensure a “measure of good government” for Northern Ireland.
The party said it would continue the discussions as it believes “devolution is best for Northern Ireland”.
But it warned it would not be a part of a “bad agreement cobbled together to suddenly suit the timetables of others”.
Sinn Féin has said a deal “can be done”, but the DUP has said that will only happen when the nationalist party drops its “red-line demands”.
Sinn Féin President Gerry Adams, Mary Lou McDonald and Pearse Doherty have joined the party’s negotiating team in Belfast.
Northern Ireland secretary James Brokenshire and Irish Foreign Affairs Minister Simon Coveney have held meetings with the political parties throughout the day.
Shadow Northern Ireland secretary Owen Smith said a decision to implement direct rule would be a “major backward step”.
Alliance Party leader Naomi Long said MLAs should face a 30% pay cut if a deal to restore devolution is not done this week.
MLAs have received their full salaries even though the Northern Ireland Assembly has not been operating during the deadlock.
Mrs Long said: “There was a previous assessment that about 70% of what an MLA does is outside the assembly and about 30% is in legislation.
“I think it’s about time that the salary was readjusted, at the very least, to reflect that.”
The cost of running Stormont in the interim has been controversial, with many commentators calling for MLAs’ salaries to be stopped.
Last month, Mr Brokenshire said that assembly members’ pay would need to be examined in the absence of devolution.
Smaller parties have complained that they have been excluded from the talks between the DUP and Sinn Féin.
The Ulster Unionist MLA Doug Beattie said: “We are, regrettably, going towards direct rule, and that is a real shame because devolution is a real positive for Northern Ireland and we should try and make that work.”
But the SDLP leader Colum Eastwood warned against a move towards direct rule from Westminster.
He has suggested a “joint stewardship” arrangement involving both the UK and Irish governments.