The DUP is understood to have received clarification from the British and Irish governments on key issues relating to a potential deal to restore devolution.
The Rev Ian Paisley's party and Sinn Féin were provided with updated texts thought to represent "the best collective effort" of Dublin and London, during a day of continued intense high-level contacts, according to a source.
Officials hope yesterday's contacts will set a positive tone ahead of Dr Paisley's meeting with British Prime Minister Mr Tony Blair on Monday.
British officials in Downing Street and at Stormont were anxious to avoid the impression that Dr Paisley had been given the governments' final word on any issue or that Monday represented an absolute deadline.
"We're not hooked on any particular day of the week," said one. "But this can't be an open-ended process either." Another said things were moving "along the right line" perhaps towards "some sort of conclusion towards the middle of next week".
The Sinn Féin president, Mr Gerry Adams, said "decision time" had arrived for the British and Irish governments and for Dr Paisley. He said the prime minister realised the importance of Monday's meeting.
"This is a hugely important opportunity that should not be missed," he said. Sinn Féin had made "its final representation to the governments on the draft outline for a comprehensive agreement", he added.
At his Falls Road headquarters Mr Adams told The Irish Times: "I presume he will seek to persuade Ian Paisley of that.
"But Mr Paisley isn't stupid he must know that he has this opportunity. Of course he has a difficult job, there are people within his constituency because change is scary - who mightn't like what is happening. People within his constituency have been hurt in the last 30 years.
"But he is a leader, and to be leader-like you have to take decisions and move forward. I hope he makes the right decision."
Downing Street confirmed: "All sides see this as an important moment." Difficulties persist over photographic evidence of IRA decommissioning. Mr Adams claimed that DUP commitment to power-sharing was also unresolved.
Dr Paisley's position on photographic evidence was seen to have hardened over the weekend, but Sinn Féin insists the matter can be resolved "to the satisfaction of all reasonable people" using the mechanisms provided by Gen John de Chastelain's decommissioning body.
The highly sensitive issue followed a series of developments which some unionists saw as concession-granting to republicans. These included movement on the Northern Ireland electoral register, demilitarisation, plastic bullets and, significantly, the release of the killers of Det Garda Jerry McCabe.
In Newry, Co Down, yesterday, the Minister for Foreign Affairs, Mr Ahern, said Det Garda McCabe's killers would not be released early unless and until paramilitarism had ended.
He agreed prisoners could get early release if a comprehensive political deal on the North was achieved. He added it was one of the unpalatable things that might have to be done if the deal was to be sealed.
Mr Adams refused to be drawn on the possible release of Det Garda McCabe's killers.
"I'm totally sensitive to the feelings of the McCabe family and particularly to his widow and therefore I'm not going to get into any of this. This is a very difficult issue, but it is one that needs to be resolved and, under the Good Friday agreement, is an issue which should have been resolved."