Sinn Fein President Gerry Adams has said he believes the DUP is prepared to sign up to a deal to restore devolution in Northern Ireland.
Gerry Adams said he believed a deal with the DUP was possible
But Mr Adams said agreement could be reached more quickly if Ian Paisley would engage in direct talks.
The DUP leader has repeated his demand for proof of IRA decommissioning if the party is to sign up to any deal.
Mr Adams said his party wanted to be "agents of change" but, like Mr Paisley, they also wanted a fair deal.
The British and Irish Governments want Sinn Fein and the DUP to have decided by Tuesday whether to sign up to a new power-sharing deal.
Speaking on the BBC's Breakfast with Frost programme on Sunday, Mr Adams said: "We can get an agreement, despite the refusal of Ian Paisley to talk."
Mr Adams said people were "hugely sceptical" that Mr Paisley would do a deal but added: "I think he will do a deal.
"But there is a responsibility on the British Government to press ahead with the Irish Government on all the outstanding aspects of the Agreement."
Ian Paisley says his party will walk away if a deal is not right
Later, Sinn Fein chairman Mitchel McLaughlin suggested the parties were "on the verge" of making a breakthrough.
"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
The comments came a day after Mr Paisley told party members in County Antrim, that it was crucial that the destruction of IRA weapons was "transparent and conclusive".
The DUP leader also warned that he would walk away from any deal he does not consider to be a fair one.
Mr Paisley is to meet the head of the decommissioning body to discuss the possibility of IRA disarmament on Monday, a move which has been welcomed by Sinn Fein.
The meeting with General John de Chastelain will come amid further talks to try to restore devolution to Northern Ireland.
Meanwhile, Catholic Primate Sean Brady has appealed to all those involved in the negotiations to grab the current "opportunity" as it offered hope for a new beginning.
Taoiseach Bertie Ahern has said the weekend would be a crucial one for the political process, and the governments would be in touch with the parties by Monday.
US president George W Bush has also offered his support to efforts to achieve a breakthrough in the political process.
Mr Bush telephoned Mr Paisley on Friday as Sinn Fein and the DUP were receiving the governments' responses to their queries over the British-Irish joint proposals.
President Bush said he had sought to get Sinn Fein and the DUP "to the table to get a deal done to close the agreement they'd been working on for a while".
Mr Blair also held further talks with Sinn Fein President Gerry Adams on Friday.
Meanwhile, more details have emerged of British-Irish proposals to deal with the demand for visible decommissioning.
Decommissioning pictures would be held until March
Talks sources suggest that by the end of December, General de Chastelain could report that all IRA weapons have been "put beyond use".
Photographic proof of this would be held by the head of the Independent International Commission on Decommissioning until March.
This would open the door to a shadow assembly at the start of January.
There would then be a new power-sharing executive.
Two churchmen - agreed by the DUP and republicans - would witness the acts of decommissioning.
It is not yet known how much of this will be agreed to by the parties, although the DUP is saying no deal will be made without photographs.
The two governments have said they are ready to publish their proposals if the parties do not sign up to a deal.
At the conclusion of intensive political talks at Leeds Castle in Kent in September, Mr Blair and Mr Ahern said the thorny issues of IRA disarmament and future paramilitary activity appeared to be resolved.
But, the two governments were unable to get the Northern Ireland Assembly parties to sign up to a deal over power-sharing after unionists and nationalists clashed over future devolved institutions.