Sinn Féin's Conor Murphy says talks at Stormont have entered a key phase as both the UK and Irish governments arrive in the hope of progress.
Secretary of State James Brokenshire and Ireland's Foreign Affairs Minister Simon Coveney are in Belfast to resume discussions after a late night of negotiations.
They believed there have been areas of agreement between the DUP and Sinn Fein, during talks aimed at restoring power-sharing.
Mr Coveney tweeted that "everyone (is) working hard to get a deal across the line".
Mr Brokenshire has extended the deadline for the parties to reach agreement and will review the situation on Tuesday night.
The parties were warned by the Secretary of State they had until Monday to produce a written agreement or he would be forced to legislate for a budget for the region at Westminster.
However, he decided on Monday night that the parties had made progress and he was going to defer his decision.
In a statement, he said: "The parties have made further progress during the course of (Monday). They are making certain additional requests of the UK Government which we need to consider.
"In the light of this, I believe it is right to defer the assessment on whether to introduce legislation to Parliament this week to enable an Executive to be formed.
"The parties will recommence talks in the morning (Tuesday) and I will reassess the position (on Tuesday) night."
The Northern Ireland Executive collapsed in January and the region has been without a power-sharing government since then.
Despite endless rounds of discussions, a deal to restore devolution has proved elusive, with the introduction of an Irish language act seen as a key issue.