Mr Tony Blair spoke by telephone to the leaders of the main political parties in Northern Ireland yesterday to express his confidence that the people had voted for a "new politics".
A spokesman for the British Prime Minister said Mr Blair believed the UUP leader, Mr David Trimble, was doing "exceptionally well" under very difficult circumstances.
He said Mr Blair was very confident about the future in Northern Ireland following the election. "The Prime Minister found amongst the party leaders he spoke to a very strong belief that the Assembly can work and is absolutely determined that it will."
Commenting on Mr Blair's telephone conversation with the Rev Ian Paisley last night, the spokesman said: "It was a perfectly friendly conversation, but the Prime Minister took the opportunity to reiterate that he wanted the Assembly to work and he hoped the parties in the Assembly would try to make it work."
The Northern Secretary, Dr Mo Mowlam, praised Mr Trimble's courage and said she would do everything she could to help him during this difficult time.
Speaking on the BBC's On the Record programme, she said: "Decommissioning is an essential part of this agreement. It has to happen, otherwise we won't have a process. But I'm not going to put down preconditions. It's what the previous government got on a hook on, and that is not helpful."
Earlier Mr Trimble warned that the Assembly was in for a tough time. "I have never concealed the fact that there are going to be problems. It's going to be a bumpy ride. It has been a bumpy ride," he said on BBC's Breakfast with Frost.