Mr David Trimble this morning said the IRA must put its weapons beyond use permanently if he is to return as Northern Ireland First Minister.
Mr Trimble, leader of the Ulster Unionists, stepped down from the job at midnight last night over the failure of the IRA to disarm.
In his first public appearance since his resignation, Mr Trimble said the IRA had missed two deadlines for the full implementation of the Agreement - May 22dn last year and June 1st 2001.
"It is for that reason because I can no longer have any confidence in the promises, the unfulfilled promises made by republicans, and because I wanted to ensure that there could be no question of the process moving beyond this without the (arms) issue being properly settled that I have now ceased to be First Minister in Northern Ireland," he declared.
"I am prepared to resume that office but only if we get this issue settledand we see weapons being put permanently beyond use in accordance with the decommissioning legislation.
"That will have to be done and we will have to be sure that the Agreement is going to be properly adhered to and not traduced."
Mr Trimble was speaking in Thiepval in France where he was attending a Battle of the Somme Commemoration.
Mr David Trimble this morning stood down as Northern Ireland's First Minister, setting off a six-week countdown to find a solution to the IRA disarmament row.
Sir Reg Empey has been appointed to take over the functions of the post, leaving six weeks for either the reinstatement of Mr Trimble or other moves to prevent the collapse of the institutions afterwards.
His appointment will allow meetings of the power-sharing executive to take place, co-chaired by SDLP deputy leader Mr Seamus Mallon - until last night the Deputy First Minister.
Yesterday, Sinn Féin president Gerry Adams claimed Mr Trimble's "kamikaze politics" were not going to achieve his objective of IRA decommissioning.
And as the height of the always-tense marching season loomed, Taoiseach Bertie Ahern warned against allowing a political vacuum to develop during the "worst two weeks of the year".
Meanwhile, GenJohn de Chastelain is due to present his latest report on weapons decommissioning to the Government later today, with its publication due to follow early next week.
Prime Minister Tony Blair said he was sorry to hear of Mr Trimble's resignation but hoped he would soon be reinstated as First Minister.
"I am sorry that David Trimble has resigned today as First Minister although I fully understand the reasons why he has felt it necessary to do so," he said.
PA