Irish unity cannot be built on violence and pain, the Taoiseach Mr Ahern said at the weekend.
He said the IRA would show it had "come round to accepting this peaceful analysis" if it followed July's formal ending of its campaign with what he called "necessary actions".
Addressing an Eamon de Valera commemoration in Co Clare, Mr Ahern said it was important to acknowledge the role de Valera played in the aftermath of the Civil War "in persuading the majority of republicans to lay down the gun in the knowledge that circumstances had changed and that it was time to move on".
He added: "By the time our mandate is complete in 2007, I am determined that there will be three enduring legacies from our terms in office: lasting peace in Northern Ireland, irreversible economic and social progress and honest and open politics in 21st century Ireland."
DUP leader Ian Paisley yesterday also pressed for the "putting beyond use" of all IRA weapons in a transparent manner. He said the IRA was still unwilling to permit photographic evidence and was insisting that it, not others, appoint one of the two independent clergymen to witness the process.