Government insiders indicated there was "no deal on the table" for the republicans but insisted lines of communication were open and played down claims that key players were being hauled into No 10 over fears power-sharing is on the brink of collapse.

Anger over the failure to complete devolution of criminal justice by the May deadline has been seen as the final straw for Sinn Fein members, who are already deeply unhappy with stalled education reforms and the handling of the Maze project, and they are set to bring down the executive by forcing an election.

Speculation is mounting that Sinn Fein is being ripped apart by internal divisions sparked by pro- and anti-assembly camps.

Yesterday's meeting, however, has also major implications for Mr Brown as it signalled the start of yet another potential crisis he must tackle as he fights for his political survival.

The Prime Minister and Mr Adams refused to comment yesterday after the private meeting.

But a government source said: "They will continue discussions to sort out the issues, that is the main thing.

"There was a very wide-ranging discussion and about how this can be moved forward.

"They are talking and trying to find a way around this. We will do whatever we can to resolve this.

"They were full and frank discussions. It is an on-going dialogue. It is not perceived as reaching crisis point."

The DUP's Peter Robinson was due to hold talks with the Prime Minister late last night on potential new contracts for Bombardier Aerospace in Northern Ireland but Mr Brown was expected to use the meeting to raise the issue of the dispute.

A DUP spokesman said: "We are open to discussions on all issues and resolutions that are acceptable to our electorate. We are not going to be pushed or cajoled in anything. That is not the way we operate."

Executive procedures mean the First and Deputy First Minister roles are inextricably linked together, which means Martin McGuinness must be re-nominated by Sinn Fein to the role. If they refuse to do that it means Mr Robinson cannot formally take up his position.

There would then be a seven day "period of grace" which would allow both sides to try to find a resolution but failure would mean Secretary of State Shaun Woodward would be forced to step in and could have to call an election to break the deadlock.

The DUP suffered a drubbing at the Dromore by-election and Sinn Fein could be banking on their reluctance to fight an election.

But a DUP source said: "Whether Sinn Fein nominate or not, it's not of huge concern to us. We are ready to fight an election.

"It is not a wise course of action for them to take and I think some of the brains in the party will bring them to their senses.

"But I think it is causing alarm for the government. Gordon Brown cannot afford to have Northern Ireland start to crumble as well as the other problems he faces."

Earlier Martin McGuinness said: "Obviously you all know that discussions are taking place on an ongoing basis to deal with the outstanding issues that St Andrews threw up and that's exactly where things are at."