The Government has been presented by the SDLP leader, Mr Mark Durkan, with a plan to revive the Northern Ireland Assembly.
Following a meeting with the Taoiseach, Mr Ahern, yesterday, Mr Durkan said the SDLP wanted to get "as much of the Good Friday agreement operating as possible".
Under the SDLP proposal, the Assembly would be revived, and politicians would hold ministerial office, though it is not clear if they would sit as an Executive.
However, he declined to indicate how ministers would be selected because he acknowledged that the D'Hondt proportional system would not be used.
"The Assembly would not operate like a local council, as the DUP wanted, and as the Ulster Unionists wanted in the past," he told The Irish Times yesterday.
The plan would not be dependent upon the IRA decommissioning weaponry in advance. "This is about getting as much of the agreement up and running again, even if other parties don't play their part in ending paramilitary activity or working the agreement."
Speaking after his meeting with the Taoiseach, Mr Durkan, stated: "The SDLP doesn't want to wait until after the summer to make progress. We don't want this drift to go on any longer.
"We are 18 months in suspension. The British government is on a go-slow on implementing the agreement.
"The North-South agenda isn't moving. The human rights agenda is at sea. This is not what the SDLP set out to achieve and is not what we can accept.
"The SDLP wants all the agreement back up and running again. But if parties are not going to agree to work the agreement or play their part in ending all paramilitary activity, then the SDLP has to seek as much of the agreement as possible.
"Indeed we believe that we can still end suspension and even get more of the agreement than we had before," Mr Durkan said.
SDLP European Parliament election candidate, Mr Martin Morgan, said: "We told the Taoiseach of our anger at Tony Blair's attempts to avoid a Finucane inquiry. We reminded the Taoiseach that it was the Irish Government that proposed bringing in Judge Cory.
"Further the Irish Government promised along with the British government that if Judge Cory recommended a public inquiry, one would be held. There is therefore a heavy onus on Bertie Ahern to ensure Tony Blair lives up to his word," Mr Morgan added.
Mr Durkan said the Taoiseach had indicated that he would follow up on the Cory Report in his meeting on Sunday with Mr Blair in Dublin.