The leader of the Ulster Unionist Party, Mr David Trimble has welcomed President Bush's words as "very positive and supportive".
Reacting to President Bush and British Prime Minister Mr Tony Blair's news conference at Hillsborough Castle, Mr Trimble said: "The strong signal given by President Bush to Irish Republicans is that 'time is running out' and they must do what is now long overdue."
Mr Trimble said Mr Bush's "explicit, frank and candid" approach was one which the party wholeheartedly welcomed.
"Republicans have been given a road map to democracy. I strongly urge them to heed the message and finally shake off the shadow of the gunman that has haunted this community for far too long," Mr Trimble said.
"On a personal level, I want to register my thanks for the commitment demonstrated by President Bush and to once again congratulate him and our own Prime Minister for the manner in which they are prosecuting the war against the Saddam regime in Iraq," he added.