Pro-Agreement parties in the North have generally welcomed efforts by US President George W Bush to put the peace process back on track.
Mr Bush, along with the Taoiseach and the British Prime Minister hosted round-table talks with the parties earlier and issued a joint communiqué saying proposals from Dublin and London "hold out the prospect of enormous progress".
The proposals are due to be unveiled on Thursday by Mr Ahern and Mr Blair.
Speaking after the round-table talks, the Ulster Unionist Party leader Mr David Trimble said he welcomed Mr Bush's "encouragement" towards achieving a solution and said Mr Bush told him he was confident that there was "an end to the process."
Party colleague, Sir Reg Empey said Mr Bush told them he felt that what had been achieved in Northern Ireland would "set an example" for the Middle East and that it could "act as a role model" for conflict resolution around the world.
Sinn Féin president Mr Gerry Adams said he had "frank discussions" with Mr Bush said he was confident that a deal could be achieved but said "critical matters" need to be addressed.
He called on all parties to "collectively lift the weight" of the problems facing the peace process.
He refused, however, to be drawn into speculation that a deal could be achieved by Thursday.
The SDLP was less upbeat about Mr Bush's visit. While welcoming Mr Bush's interest in the peace process, SDLP leader Mr Mark Durkan said that the real serious discussion would come in the next few days.
"We don't need people helicoptering and flying in and out of here to speak to us about common sense," he said.
Mr Durkan said the SDLP also took the opportunity to raise their objection to the war in Iraq with Mr Bush.
Ms Monica McWilliams of the Women's Coalition, was visibly frustrated after her meeting with Mr Bush and Mr Blair. She said they had "heated discussion" during which she told them her party had wanted them to go down the diplomatic route to find a solution to the Iraq conflict. "We left them in no uncertain terms that we were against the war," she said.
Earlier, the Sinn Féin president handed a letter Mr Bush and Mr Blair a letter detailing his party's opposition to war in Iraq.
Mr Trimble reacted caustically to Sinn Fein pleas for peace. He said he found it "ironic" and "hypocritical" that many of those demonstrating against military action in the gulf had been supporters of "the dirty little terrorist war here".