President Clinton has appealed to the people of Northern Ireland not to let the present hope for peace "slip away". He said "it will not come again in your lifetime".
In a speech at the start of his one-day visit to the North, Mr Clinton both painted glowing hopes for the future and issued warnings about difficult times to come.
"This has been a magic thing to see unfold - this developing will for peace among the people. Together, people and leaders are moving Northern Ireland from the deep freeze of despair to the warm sunlight of peace."
Addressing an audience of some 2,000 in the new Waterfront Hall in Belfast, the President also appealed to members of the new Assembly present to avoid fighting among themselves.
"Whenever possible, you must try to act in concert, not conflict; to overcome obstacles, not create them; to rise above petty disputes, not fuel them."
In a speech in which he tried to sound mostly inspiring and optimistic, Mr Clinton also struck a sombre note when he warned there would be "hard roads ahead".
He declared with apparent certainty that "the terror in Omagh was not the last bomb of the Troubles; it was the opening shot of a vicious attack on the peace.
"The question is not whether there will be more bombs and more attempts to undo with violence the verdict of the ballot box. There well may be." He said there would also be divisive debates.
The question was how the Northern Ireland people would deal with future differences. "Can the bad habits and brute forces of yesterday break your will for tomorrow's peace?" Mr Clinton asked.
The President did not try to answer the question but finished with a portrayal of a community which should be more united than divided. In a rhetorical flight he told his almost exclusively middle-class audience: "You aspire to the same things - to live in peace and security, to provide for your loved ones, to build a better life and pass on brighter possibilities to your children. These are not Catholic or Protestant dreams, these are human dreams, to be realised best together."
Mr Clinton was given a standing ovation when he was introduced by the First Minister and Ulster Unionist Party leader, Mr David Trimble. Earlier, there had been speeches by the British Prime Minister, Mr Tony Blair; the Deputy First Minister, Mr Seamus Mallon; and Belfast's Lord Mayor, Mr David Alderdice.
Among those listening to the President's address were Mrs Hillary Clinton, Mrs Cherie Blair, Mrs Trimble, former senator Mr George Mitchell, who received three separate ovations, and the Northern Secretary, Dr Mo Mowlam.
In his speech, Mr Clinton promised continuing US support for the peace process "in the months and years ahead".