Peter Robinson is set to meet the Prime Minister today for crunch Downing Street talks on the latest Stormont crisis.
It comes after the UUP voted to quit the power-sharing Executive at the stroke of midnight in the wake of revelations that the Provisional IRA still exists.
It is believed the DUP wants David Cameron to ensure that any former paramilitary prisoners released under the Good Friday Agreement but who are suspected of criminal activity are returned to jail.
The row comes after PSNI chief constable George Hamilton said the IRA still exists and some members were involved in the recent murder of Kevin McGuigan.
Mr Robinson has branded the UUP decision irrational, illogical and based on "political expediency" rather than principle.
But the controversial move by Ulster Unionist leader Mike Nesbitt has received the strong backing of one of his predecessors, former First Minister Lord Trimble.
As the war of words continued, Lord Trimble said: "Something has to be done and I'm not sure Robinson can do it. He is talking about somehow excluding Sinn Fein but that can't be done immediately."