Sinn Féin is urging the Dublin and London governments to take a strong line with the DUP following its strong performance in the recent elections to the Belfast Assembly in the North.
A long political stalemate is threatened as Ian Paisley's party moves slowly to chart the political waters ahead of a review of the 1998 Good Friday Agreement next month.
The DUP is opposed to the Agreement, which remains only partially implemented. It is demanding the Agreement be renegotiated, possibly from scratch.
It is understood this would mean that - alongside the review starting next month - there should be high-profile meetings of the Anglo-Irish Inter-Governmental Conference in Belfast and Dublin. These would mark a renewed push to implement commitments in the British-Irish Joint Declaration of last April on a range of issues including demilitarisation, criminal justice reform, on-the-run prisoners, and the structure of the North's Human Rights Commission.
The party is determined there should be progress on the implementation of the outstanding aspects of the agreement In particular, Sinn Féin leaders wish to resume their pre-election discussion with both governments about the unresolved issue of policing and the party's attitude to joining the Policing Board.
Sinn Féin's national chairman Mr Mitchel McLaughlin,in London, insisted Dr Paisley's victory required London and Dublin to spell out "the options to the rejectionists".
"No longer can Mr Blair use David Trimble's precarious hold on leadership of majority unionism to justify prevarication," McLaughlin said. "He must act decisively to disavow rejectionists of the notion that they can renegotiate the agreement."
Sinn Féin, the UUP and other parties are also believed to be considering changes to the Assembly's cross-community voting rules to enable the appointment of a power-sharing Executive despite DUP opposition.
In a situation in which the DUP's unionist majority has a veto over the election of first and deputy first ministers, some rule change would be necessary to prevent a re-run of last month's Assembly election.
The cross-community Alliance Party today ruled out redesignating its Assembly members as unionists to help set up a power-sharing government.
Alliance leader Mr David Ford, whose party was fortunate to hold on to its six Assembly seats on a reduced vote, rubbished the suggestion.
"I have repeatedly made clear that there are no circumstances whatsoever in which Alliance will redesignate.
"The two governments [in Dublin and London] are very well aware of our views on the matter. At least they seem to know better than to raise the issue."