The political parties said they were willing to continue work throughout July if it led to political progress.
The DUP, which was first to meet Taoiseach Bertie Ahern and British prime minister Tony Blair, insisted that the Assembly should debate the issues blocking the return of devolution before negotiations restart in the autumn.
"If negotiations are going to begin in the autumn, then the Assembly is going to have to meet between now and then," DUP deputy leader Peter Robinson said.
"We cannot move on to the next stage unless we move in the sequence of 'scoping' the issues, debating the issues [ in the Assembly] and then negotiating the issues."
Sinn Féin did not oppose this suggestion outright when asked if its MLAs would end their boycott of the Assembly. Party president Gerry Adams said if the Rev Ian Paisley's party wanted to propose such a debate at the next meeting of the Preparation for Government Committee at Stormont next week, his party would listen to the argument before arriving at a considered conclusion.
Speaking after meeting the two premiers, Dr Paisley denied his party was under any pressure to deal with Sinn Féin and form a powersharing government.
"There is no change in our policy," he said. "They [ the governments] can say what they like, we are standing firm."
He denied Mr Ahern and Mr Blair emphasised any deadline for progress before the Assembly was put into "cold storage" after November 24th.
"The situation remains that IRA/Sinn Féin are a terrorist organisation; they have not conformed to the principles of democracy," he added. Nor had they backed policing or the administration of justice.
It was up to Sinn Féin to make the important decisions, he said. The DUP had nothing else to add.
Dr Paisley also revealed that the late Mgr Denis Faul had communicated to him shortly before his death that the DUP leader should press harder for the IRA to give up the bodies of the "Disappeared" as part of its demands.
Sinn Féin president Gerry Adams said the two governments had sought to reassure republicans "of their total commitment to the November 24th deadline and their commitment to making this process work", he said.
"We now want them to match that verbal commitment with action in the time ahead," he said.
"For our part, we told the Taoiseach and the British prime minister that they must act to bring about the full implementation of the Good Friday agreement. Words are not enough."
Ulster Unionist leader Sir Reg Empey said those who had no intention of meeting the November 24th deadline should "have the guts to say so".
SDLP leader Mark Durkan said he did not believe other parties thought the November 24th deadline would be imposed.
"There still is a major problem in that other parties think that they can posture, delay, buy more time and create more difficulties," he said.