UUP deputy leader Danny Kennedy has said his party accepts the account given by witnesses Fr Alec Reid and Reverend Harold Good of IRA weapons decommissioning.
The Taoiseach and the Sinn Féin President said the DUP leader, Ian Paisley, should be given time to reflect on yesterday's announcement that the IRA's weapons have been put out of use.
Bertie Ahern and Gerry Adams were responding separately to Dr Paisley's assertion that there was still no proof that all the IRA's weapons have been decommissioned.
Mr Ahern added that further reports from the Independent Monitoring Commission would show that the peace process had moved to a new phase.
Mr Paisley also asserted that the gun is not out of Irish politics.
Dr Paisley was speaking after meeting the head of the decommissioning body, General John de Chastelain, in Belfast.
The meeting was part of a series of meetings today involving General de Chastelain and Northern Ireland's political parties to discuss in greater detail the destruction of the IRA's arsenal.
General de Chastelain, along with fellow members of the International Independent Commission on Decommissioning, was also due to meet delegations from the Ulster Unionists, the SDLP and the Alliance Party.
Meanwhile, the Sinn Féin Chief Negotiator, Martin McGuinness, is travelling to the United States to brief politicians on the latest developments.
Last night, the Northern Secretary, Peter Hain, said unionist distrust is natural, but he insisted that the IRA's move would bring the return of devolution closer.
A spokeswoman for Mr Ahern said that the UN Secretary General, Kofi Annan, telephoned Mr Ahern to congratulate the Government on yesterday's announcement.
The Taoiseach hopes to meet the British Prime Minister, Tony Blair, in the coming week to discuss how to move forward in Northern Ireland.
The Dáil is to hear statements on the most recent developments when it returns tomorrow.
