The Sinn Féin leader, Gerry Adams, has appealed for direct talks with the DUP leader, the Reverend Ian Paisley.
Mr Adams was speaking at a news conference following yesterday's assessments given by the Taoiseach and the British Prime Minister on the state of the Northern Ireland peace process.
Speaking on RTÉ's News At One programme, DUP MP Jeffrey Donaldson said his party could do nothing more to bring about verifiable IRA decommissioning. Instead, he called on Mr Adams to speak with the grassroots of the IRA to bring this about.
Yesterday, Bertie Ahern and Tony Blair confirmed that the latest settlement formula put forward by both governments had foundered on the issue of photographic evidence of IRA decommissioning.
However, both leaders stressed their determination to continue with efforts to reach an agreement on the restoration of power-sharing in the North.
Mr Ahern said he believed an agreement was still possible while Mr Blair said he thought it was inevitable.
Dáil debate promised
Meanwhile, the Tánaiste Mary Harney has promised a Dáil debate on the North to take place next week.
Earlier, party leaders Enda Kenny of Fine Gael, Labour's Pat Rabbitte and Trevor Sargent of the Greens, all expressed regret that talks to restore devolution had failed.
Sinn Féin TD Caoimhghín Ó Caoláin was heckled as he praised the work of the leaderships of Sinn Féin and the IRA for their contribution to the peace process.
Ms Harney replied that she would not applaud anyone who had maimed and killed in the name of Ireland.
NI party talks
Foreign Affairs Minister Dermot Ahern said he and Northern Secretary Paul Murphy will meet all the North's parties next week to try to find common ground in the wake of the failure to agree a deal.
Mr Ahern said he remained confident a deal could be reached and added that the work of the Irish and British governments so far represented a considerable achievement.
The minister said they must now try to find if there is any middle ground between the diametrically opposed views of the DUP and republicans.
Response to IRA reaction
Other political and church leaders have been responding to the IRA's reaction to developments in the peace process.
In a statement issued through the republican newspaper, An Phoblacht, the IRA claimed that taking photographs of the completion of the destruction of its weapons would be impossible.
It also described the suggestion as a process of humiliation.
The organisation also claimed that Mr Paisley had insisted on photographic evidence as an excuse for his rejection of the deal to revive power-sharing.
Settlement founders
This morning, the Catholic Primate Archbishop Dr Seán Brady, said he shared the disappointment of others that a deal had not been possible.
He observed that more trust had to be built and said he was very encouraged by the willingness of the governments to continue the search for a deal.
Meanwhile, Sinn Féin National Chairman Mitchel McLaughlin said his party stretched itself to the limit to try to bring about agreement.
Speaking on RTÉ's Morning Ireland programme, Mr McLaughlin described the issue of photographing IRA decommissioning as 'a bridge too far'.
He said the additional offer of two clergymen witnesses made by the IRA in this morning's statement was an honourable compromise.
