The Ulster Unionist leader David Trimble has said he believes there is "every prospect" of a settlement which would see a return to stable power-sharing institutions in Northern Ireland.
However, he warned that so long as the IRA held on to its weapons, the process would remain in crisis.
Mr Trimble was speaking the day after it was announced that US President George Bush would join the Taoiseach Bertie Ahern and the British Prime Minister Tony Blair in the North next week for a high-profile bid to give renewed impetus to the peace process.
Mr Ahern and Mr Blair are expected to produce a new formula to bring about the full implementation of the Belfast Agreement, five years after it was signed, and it is thought that Mr Bush's presence may put added pressure on pro-Agreement parties to reach consensus.
It is understood that the success of the initiative will hinge on the readiness of the IRA to announce a major move on decommissioning within the coming days or weeks.
Mr Trimble said that the new formula should enable the Republican movement to "take the final steps in the transition" away from violence.
However, he made clear that the UUP would not be prepared to accept an amnesty for IRA fugitives - one of the key demands of Sinn Fein.
But he indicated that the party was ready to accept an arrangement to defuse the issue, by having 'on-the-runs' return to jail only to be freed under the early release scheme. Those who had never been convicted should face "some judicial proceedings", he said.
Mr Trimble suggested that Mr Bush's visit was primarily linked to the war in Iraq, saying that the President and Prime Minister would have only a "brief chat" with the Ulster parties during their talks.
But he said that Mr Bush kept himself briefed on developments in Northern Ireland and had met representatives of the parties in the Oval Office recently.
PA