Sinn Féin chairman Mr Mitchel McLaughlin has suggested the DUP and his party were "on the verge" of making a breakthrough.
Speaking on BBC Radio 4's World This Weekend,he said: "This has been a successful peace process - perhaps one that didn't develop as quickly as people on the ground would have hoped, but nonetheless it has been moving steadily in the right direction, despite all the hiccups and frustrations and disappointments.
"The final piece in bringing all-party dialogue about is this discourse between the DUP and Sinn Fein and I think we are on the verge of achieving that."
Mr McLaughlin acknowledged that there were many unresolved issues on all sides of the community relating to the traumas of the past 30 years.
But he said: "All, I think, are now coming to the view that what we have to do is move into new space, create a new future. We have had enough of a history and a past of conflict and division.
"On that basis of equality, let's address the legacy issues and let's draw lessons from it to make sure it doesn't happen again."
Earlier the Sinn Féin president Mr Gerry Adams said he believed the Reverend Ian Paisley would eventually strike a deal with his party despite the scepticism of nationalists.
But the West Belfast MP insisted any move on weapons was a matter for the IRA and General John de Chastelain to work out.
"The reality is under the Good Friday Agreement there is a commission," he told the BBC's Breakfast with Frost programme.
"That commission is responsible for verifying and overseeing the putting of arms beyond use or the decommissioning of arms.
"The IRA is the only organisation - and this has caused huge difficulty for many republicans and nationalists - to have actually engaged with that international, independent decommissioning body.
Meanwhile the leader of the Green Party has said the unique chance to strike a deal had to be seized by all parties.
"The opportunity that this period represents is going to be very difficult to revisit if the nettle isn't grasped on both sides," Mr Sargent said.
"There isn't the luxury of a suck it and see, or procrastination, it's important that politics is seen to work and is accessible to everybody."
Mr Sargent said failure to reach agreement would be felt hardest by people living in interface areas across Belfast, with tensions rising the longer the deadlock lasted.
PA