Concessions on offer from the Provisional IRA raise the question of whether the DUP is "genuinely" prepared for partnership politics, the Taoiseach, Mr Ahern, has said.
Mr Ahern said last night current negotiations offered the real prospect of an historic end to paramilitary operations by the IRA and the rapid completion of decommissioning.
However, he said the finalisation of the offer from the IRA was available only if the DUP fully accepted partnership within Northern Ireland and in the North-South bodies.
With the talks now within two weeks of the latest deadline for agreement, Mr Ahern said the Irish and British governments will put forward their final proposals in the coming days.
He stressed that the DUP had an unprecedented opportunity to consolidate peace and political stability in the North, but warned that this opportunity might be lost if unrealistic demands were made of the IRA.
"It would be tragically ironic if the prospect of ending IRA activity and capability was lost because it did not meet unrealistic thresholds of visibility," he said.
Addressing students in Trinity College, Dublin, the Taoiseach called on the DUP to take part in the power-sharing institutions and to devolve policing and justice powers to the power-sharing assembly.
"These raise challenging questions for the DUP, specifically, whether they are genuinely up for partnership politics or not," he said.
Any attempts to "hollow out" the power-sharing provisions and protections of the Good Friday agreement will not be acceptable and will not work, he said.
Mr Ahern said the Government needed to ensure that decommissioning had the confidence-building impact required within the unionist community.
He recognised that some additional elements of transparency may be required and said that it ought to be possible to agree "reasonable steps" if there is a will to reach an agreement.
However, he said that any unreasonable demands that carried a resonance of humiliation would be entirely counter-productive and will not work.
Mr Ahern stressed there was only a narrow opportunity for agreement but "very few" issues were outstanding.
"Both governments now believe that there exists a real prospect of definitively ending IRA paramilitary activity and rapidly completing the decommissioning of IRA weapons.
"The achievement of that prospect would transform the political environment in Northern Ireland and we are determined that it will be secured," he said. Failure to achieve an agreement would see the Irish and British governments finding a different way to move the process forward within the context of the Good Friday accord.
"We will work together on an even closer basis with our British partners to advance the agreement in every way possible."
Mr Ahern said leaders on all sides must be prepared to take risks for a final agreement but he did not believe that such risks were unmanageable for any party.
"For our part, we are prepared to accommodate changes to the operation of the Good Friday agreement so long as they are not at the expense of the fundamentals of the agreement," he said.
"If there is a will on all sides to finish this once and for all, I believe sincerely that it can be done. That requires movement from both sides to close the gaps on the key outstanding issues, including the question of acts of completion by the IRA."
