Negotiations over the issues of historical killings, parades and flags were “80 to 90 per cent” completed, the Ulster Unionist leader Mike Nesbitt said on Sunday.
“What is left is serious from our point of view,” Nesbitt said. The former US diplomat Richard Haass has urged the parties to reach an agreement on Monday.
US National Security Council spokeswoman Caitlin Hayden said: "Initiating these talks demonstrated the commitment of the parties and people of Northern Ireland to move forward on tough issues. We are confident that a solution can be reached if there is political will on all sides.
"We call upon the leadership of the five parties to make the compromises necessary to conclude an agreement now, one that would help heal the divisions that continue to stand between the people of Northern Ireland and the future they deserve."
There has been an upsurge in recent bombings and attempts to kill members of the security forces by dissident republicans opposed to the peace process, which culminated in the 1998 Good Friday Agreement.
But measures intended to ease months of simmering resentment and violence are extraordinarily close to gaining support, Dr Haass has said, adding that the missing ingredient was not more time and urging politicians to grasp the opportunity to do a deal.
A session starting at 6am on Monday will bring six months of increasingly intense negotiations to a head after the conflict resolution expert cut short his Christmas break to kick-start one last round of crunch discussions.