The Taoiseach, Mr Ahern, and the British Prime Minister, Mr Tony Blair, yesterday made it clear to the North's parties that rather than "elongated negotiations" they are seeking a comprehensive deal out of the Leeds Castle political talks.
Mr Ahern and Mr Blair referred to the public frustration at the absence of a deal and at the continual rounds of inconclusive negotiations.
They reminded the parties that it was two years since the British Prime Minister's "acts of completion" speech in Belfast and that now was the time to finalise agreement to restore devolution.
The Taoiseach said this was the third time in less than two years that the two leaders were engaged in major negotiations.
"We want to see the institutions being stable and durable to give the people of Northern Ireland an opportunity to have their own administration, their own Assembly and executive, to see all the bodies work," Mr Ahern said.
"We want to see an end to paramilitarism through decommissioning and the cessation of all paramilitary activity - and we have been around that so many times," added the Taoiseach.
The issue of devolving responsibility for policing to the Northern executive was among the problems that must be resolved, he said.
Striking a deal was about political will and leadership, he added.
Mr Ahern hoped that these talks would not just be another stage on the way to further negotiations.
"I hope we leave Leeds Castle with success, not failure. I hope we end with finality, and not just a parking spot on the way," he said.
Mr Blair described the negotiations as the "moment of decision as to whether those acts of completion" would follow from Leeds Castle.
"We need stable and durable institutions in Northern Ireland and we need to ensure that those institutions are operated on the basis of a commitment to exclusively democratic and peaceful means," he said.
It was frustrating that the politicians were still addressing the same issues. "They have not changed and this is the time we have to decide it. We can't go out of this and have another set of elongated negotiations. This really is the moment of decision for us," said Mr Blair.
"It will be a test of political leadership and political will and a test of whether we are prepared to listen in a profound way to the yearning of the people of Northern Ireland for a peace that isn't haphazard and random, that isn't partial, that is complete and total and lasting," he added.
