President Clinton discussed the next moves in the formation of the North's new political structures with Mr Tony Blair, Mr David Trimble and Mr Seamus Mallon for 20 minutes at Stormont yesterday morning.
Fears in advance that Mr Clinton's meeting with Assembly members at a reception immediately afterwards would be disrupted by robust DUP protests were not borne out. Instead, Mr Clinton had a civil discussion with Mr Nigel Dodds of the DUP about that party's objections to the progress of the peace process.
During the talks with Mr Clinton, the British Prime Minister urged the President to use his influence to get the political parties to take necessary further steps in the peace process.
The talks came as the Assembly is due to meet on Monday week amid continuing uncertainty over whether the new executive will be formed then.
Mr Trimble will consult members of his party this weekend to discuss whether he should hold a face-to-face meeting with the Sinn Fein leader, Mr Gerry Adams. Such a meeting would be seen as a further important step towards the formation of an executive containing UUP and Sinn Fein members. The issue of weapons decommissioning is the stumbling block to the formation of the executive.
According to Northern Ireland Office sources, yesterday morning's meeting concentrated on future developments, with Mr Clinton particularly keen on hearing how the Assembly would operate.
Mr Trimble and Mr Mallon are understood to have given accounts of how they believed it should work.
According to Downing Street sources, Mr Blair, Mr Clinton and Mr Mallon agreed there had been a "new mood" after the Omagh bombing and that the peace process was moving in the right direction.
A Downing Street spokesman said Mr Blair told the meeting that "recent moves on both sides had helped to build confidence and trust", and that he was "confident the peace process was in very good shape".
Mr Clinton concluded the meeting by saying the success of the peace process in Northern Ireland was "vital" both for the North and for peace processes around the world.
If it worked it would "act as an inspiration and a force of pressure elsewhere", he is reported to have said.
Mr Clinton then went to the reception held by Assembly members in the Long Gallery of Stormont's Parliament Building.
In the absence of the Rev Ian Paisley and Mr Peter Robinson, who had not returned from the Westminster debate on the new security legislation, the DUP's criticisms of the peace process were made by Mr Nigel Dodds to Mr Clinton.
Mr Dodds said he told the President he believed he was wrong in giving his support to Sinn Fein participation in the Assembly.
On the issue of decommissioning, according to Mr Dodds, "he (President Clinton) fully appreciated the issue was vitally important to the unionist population. He said he had been working very hard on the issue for the past three weeks."
Mr Clinton differentiated between Sinn Fein and splinter republican groups, but the DUP did not accept this differentiation, Mr Dodds said.
Meanwhile, President Clinton was clearly delighted with headlines greeting his arrival proclaiming that Mr David Trimble and Mr Gerry Adams are to meet soon, writes Joe Carroll from Armagh.
The decision by Sinn Fein to appoint Mr Martin McGuinness to the decommissioning body was also hailed as a sign of real progress in a peace process which was in danger of stalling.
The White House press secretary, Mr Mike McCurry, said: "When Presidents of the United States travel, it is often an action-provoking journey, and it appears that the President's journey here has helped the parties concentrate their efforts and to make some progress."
But US aides were cautious about predicting a face-to-face meeting between Mr Trimble and Mr Adams while seeming convinced that it will happen next week.
Mr Clinton has been told that it will happen next week but "we did not make any efforts to make it happen here," Mr McCurry said. President Clinton responded positively to the concern expressed by Mr Blair about possible funding from the US for the IRA breakaway groups.
He indicated that all necessary steps will be taken under existing legal constraints.
Details of all Mr Clinton's meetings with the members of the Northern Ireland Assembly were not given by White House aides.
He accepted a letter from Mr Dodds, protesting against the way terrorists have been "taken by the hand".
But the encounter was said to be polite.