DUP leader Peter Robinson has said retaining the police full-time reserve was not a precondition for the devolution of policing and justice, after republicans warned a major crisis was looming.
Earlier on Wednesday, Mr McGuinness and Mr Robinson held talks in Belfast with the Irish government's Foreign Affairs Minister Micheal Martin.
At a subsequent press conference, which Mr Robinson did not attend, Mr McGuinness indicated that failure toagree a firm deal by Christmas would have serious political implications.
"What absolutely is an imperative is to have an agreement on the transfer of power, and a date for the transfer of power, before Christmas. I have to say if it slips past Christmas we are in deep trouble," Mr McGuinness said.
But fears of an immediate crisis eased in the afternoon after Mr Robinson said: "We have made it very clear that in relation to policing and justice there is but one precondition...the necessity to have public confidence in the devolution of policing and justice powers."
After a meeting with the Chief Constable, Mr Robinson said the DUP was up for the devolution of policing and justice, but warned he would not be bullied.
He said both parties had issues that had to be resolved in talks before a final deal.
He said frontline policing must be protected and former reservists should have a chance to play a future role in the service where administrative posts are to be created.
"The resources have to be there. The gap that would be left if they were removed has to be filled by people of the experience and skill that would be removed," he said.
Earlier this week, DUP MP Jeffrey Donaldson had said axing the full-time reserve would make it impossible to agree to the devolution of policing and justice.
On Wednesday night, TUV leader Jim Allister hit out at the DUP and said: "The police reserve will go, (but)sweeten it by making some of them office boys. It is an appalling shame."
© Press Association