The discussions, which will be held in Downing Street, are expected to continue on Wednesday.
Both Tony Blair and his Irish counterpart, Bertie Ahern, have said they are determined to resolve the issues of arms, demilitarisation and policing, which are causing a stumbling block in the peace process.
Meanwhile, there has been critisicm from Sinn Fein over the postponement of a meeting of the British-Irish Council to facilitate efforts to break the political deadlock.
On Monday, party chairman Mitchel McLaughlin claimed the two governments were covering up for Mr Trimble, who, he said, was refusing to sign papers to allow Sinn Fein's Bairbre de Brun attend the meeting.
The meeting, scheduled for Dublin on Tuesday, would have been the second of its kind, with the heads of administrations throughout the British Isles due to attend.
It will now be held on 5 February.
'Crisis' claim rejected
Mr Trimble told the assembly that Tuesday's meeting had been seen by the governments as a "distraction" to the ongoing political discussions.
He said he hoped these would be successful and he rejected claims by the Democratic Unionist Party that the Good Friday Agreement was in crisis.
Mr Mallon told the assembly the reason for the postponement was to allow time for the governments to focus on the current political negotiations.
A senior government source said officials from both governments were engaged in the behind-the-scenes efforts to end the stalemate - and it was thought better that they continued to concentrate on that.
However, Mr McLaughlin described that as "nonsense".
"They are providing a fig leaf for David Trimble," he said.
He added: "He has refused to sign the authorisation.
"Clearly both governments have backed down on that."
Ulster Unionist Dermot Nesbitt said Mr Trimble had made his position clear months ago about what would happen if Sinn Fein were found to be "not fulfilling their full obligation as part of the republican movement".
"There is illegality out there. IRA terrorist weapons comprises illegality.
"We cannot have people participating, as they are at the minute, in the government of Northern Ireland and condoning illegality."
Mr Trimble refuses to authorise the attendance of Sinn Fein ministers at meetings of the North-South Ministerial Council. It is an attempt to get the IRA to substantially re-engage with the decommissioning body.
Mr Blair, who was in Belfast last week for talks with different political groups, is keen to see an end to the impasse.