The four co-chairmen of the AdHoc Committee for Irish Affairs in the US Congress have urged the Ulster Unionist Party leader, Mr David Trimble, to enter direct negotiations with the Sinn Fein president, Mr Gerry Adams.
They said it was "the consensus of most in the United States Congress" that any agreement reached at the talks must "at a minimum include North-South bodies with strong executive powers".
The chairmen issued their statement after separate meetings with the Irish Ambassador in Washington, Mr Sean O hUiginn, and the British ambassador, Sir Christopher Meyer.
The committee consists of about 60 Democratic and Republican members of the House of Representatives and is the main forum for discussing Irish affairs on Capitol Hill.
The co-chairmen are Mr Ben Gilman (Rep), who is also chairman of the influential International Affairs Committee of the House; Mr Peter King (Rep); Mr Tom Manton (Dem) and Mr Richard Neal (Dem).
The statement says: "It is obvious that for the peace process to succeed, David Trimble must realise that he has to meet with and directly engage Gerry Adams. Mr Trimble must do more than say No.
"Unlike Mr Trimble and the Ulster Unionist Party, Gerry Adams and Sinn Fein have acted honourably and responsibly throughout the talks, particularly during this period of provocative sectarian killings. If the talks fail, history will judge David Trimble and the Ulster Unionist Party as being responsible for their failure."