Sinn Fein's meeting with Tony Blair to discuss government proposals to break the political deadlock was positive, Gerry Adams has said.
Sinn Fein say the Agreement's fundamentals must not be changed
The British and Irish Governments put their proposals to the DUP and Sinn Fein on Wednesday.
In a statement on Thursday, the DUP said the latest proposals contained areas of "confusing ambiguity and even apparent inconsistency".
DUP leader Ian Paisley said he wants Mr Blair to confirm that the IRA has accepted those parts of the proposed agreement which affect its activities.
Speaking after leading a Sinn Fein delegation to meet Mr Blair at Downing Street on Thursday, Mr Adams said they hoped to agree a deal soon.
"We have been putting it to the two governments for some time that they need to come forward with propositions which are bedded in the Good Friday Agreement," he said.
"They have now come forward with propositions, and we are now seeking assurances that they are bedded in the Agreement - that shouldn't take very much longer."
Concerns are thought to include ministerial authority and the potential for north-south institutions to develop.
BBC Northern Ireland political correspondent Martina Purdy said there were faint hints that the DUP's demand for photographic evidence may be addressed in some way.
Speculation has centred on a photograph that will not be published but shown to the DUP.
The document addresses the principle of transferring policing powers to the assembly, as well as the need for community confidence before this can take place.
One source told the BBC that it did not contain a target date for the devolution of policing and justice, which is a key Sinn Fein demand.
It is thought the paper proposes beefing up the British-Irish Council, which unlike the north-south council, lacks its own secretariat or headquarters.
Both the DUP and Sinn Fein leaderships will be briefing their party members about the latest proposals on Friday.
Mr Paisley said he would be taking a few days to study the paper.
The DUP leader said: "We will also want to have clarification on a number of matters where there is a lack of detail or the use of imprecise text.
"We must not allow a lack of clarity to lead to misunderstanding and dispute at a later stage."
He added: "We will need the prime minister to confirm to us that in each and every respect the IRA has accepted the nature, extent and particulars of that part of the agreement which impacts on its activities and position."
Mr Paisley said that his party would "engage positively" with the government over the coming days in an effort to resolve outstanding matters.
Meanwhile, Senator George Mitchell - who helped to broker the Good Friday Agreement - said he thought the parties had made good progress.
"The parties have reacted with innovation and good faith in trying to come up with mechanisms to create assurances in the absence of trust," he said in Belfast on Thursday.
"I hope very much that they reach it. They appear to be quite close, from the published reports that I've read."