Ulster Unionist leader David Trimble has said he is optimistic that the political process in Northern Ireland can recover.
Talks will continue after Tuesday's setback
He was speaking as talks were set to resume on Wednesday in an effort to rescue a potential deal to restore devolution in the province.
On Tuesday, Ulster Unionists rejected the IRA's latest act of decommissioning as not being transparent enough.
Arms chief General John de Chastelain's report confirmed the quantity of weapons put beyond use by the IRA was "considerably larger" than that which had been previously decommissioned by the republican movement.
Speaking in the Irish parliament on Wednesday, Mr Ahern said he was "deeply disappointed that our efforts failed".
However, while he was very frustrated, he said it was "a new day and we have to get on with it".
Mr Ahern told the Dail that Downing Street was aware that on Tuesday morning he was reluctant to travel to Hillsborough because of concerns about the decommissioning element.
He said he had been trying to get in contact with General de Chastelain since 1830 BST on Monday, but was unable to do so until he met him on Tuesday at Hillsborough.
Mr Trimble denied pro-Good Friday Agreement unionism was in disarray, and outlined what was needed to create resolution.
0710 BST Tuesday: Downing Street announces 26 November election date
1030: Sinn Fein's Gerry Adams urges total support for political process
1215: IRA says there will be further act of decommissioning
1415: IRA says further act of decommissioning took place under agreed scheme
1600: Arms chief says a third act of decommissioning has been witnessed
1720: UUP leader says transparency over arms is needed
1820: Tony Blair and Bertie Ahern say Mr Trimble's statement is "a glitch"
1850: Sinn Fein says it is disappointed and surprised at latest events
1940: Two PMs hold talks with Sinn Fein at Hillsborough
2050: Tony Blair makes clear the assembly election will go ahead on 26 November
"It would be a very serious mistake at this stage to write this off, and I have deliberately acted in such a way as to keep this thing alive, by still providing for the unionist council to meet next week.
"Recovery would be very simple - let the prime minister put the information he has in the public domain.
"Let the republicans remove from De Chastelain the limitations that have prevented him from giving a full report - let him do so."
Prime Minister Tony Blair said on Tuesday night that assembly elections would go ahead as planned on 26 November.
Mr Blair said he was disappointed at what had happened but was hopeful that the issue could be resolved.
"I believe that if people knew the information that we have been told, yes they would be satisfied," he said.
"But it is also the case that the commission enters into certain agreements with the bodies that do the decommissioning.
"One part of that agreement, as they are entitled to do under the legislation, was a confidentiality clause on the exact specific details of what was decommissioned."
Mr Blair and Irish Prime Minister Bertie Ahern held talks with Sinn Fein President Gerry Adams at Hillsborough later on Tuesday.
Speaking after the meeting, Mr Adams said there were profound difficulties in resolving the problems.
The Sinn Fein president later met Mr Trimble at Hillsborough.
The Northern Ireland Secretary, Paul Murphy, is expected to make a statement to parliament later on Wednesday, officially confirming the assembly election will take place on 26 November.
The devolved administration at Stormont was suspended a year ago amid allegations of IRA intelligence-gathering in the Stormont government.
In a second statement on Tuesday, the IRA leadership confirmed that more weapons had been decommissioned.
In some of the strongest words the Sinn Fein president Gerry Adams has used in support of the peace process, he said Sinn Fein was "opposed to the use or threat of force for any political purpose".
Mr Adams said: "Sinn Fein wants to see the guns taken out of Irish society."
The announcement of an election date came after weeks of top-level negotiations between Sinn Fein and the Ulster Unionists, as well as the British and Irish Governments.
Sinn Fein's Mitchel McLaughlin said on Wednesday that the situation could still be salvaged if Mr Blair made a statement saying that the IRA was in full compliance with the decommissioning scheme.
SDLP leader Mark Durkan said public confidence would not be affected by the IRA waiving confidentiality over disarmament.
"The rights of the public have been waived at different times and the rights of other parties, particularly pro-Agreement parties, have been waived by those involved in all this choreography," he said.
Democratic Unionist leader Ian Paisley said the political process had descended into a farce.
"Once again, events have been over-hyped and are entirely devoid of substance. Yet again the decommissioning stunt has been shown to be nothing more than a hollow sham," he said.
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