The Taoiseach, Mr Ahern, told the Dáil that all paramilitary weapons must be put beyond use as part of a final solution in the North.
Mr Ahern said he believed there was the opportunity to bring work on the North to a finality, but he could not say when the two governments would be able to do so. "But our goal, and the goal of both governments, is to complete our work as soon as possible so that we can present the fruits of our efforts over the last several months," he added.
He said that the phrase "acts of completion" captured both the enormity and the simplicity of what was required. "It reflects an end to instability and lack of confidence, the attainment of a satisfactory finishing-point in all aspects of implementation and a completion of the transition from paramilitarism to exclusively peaceful means," he added.
Mr Ahern said that "acts of completion" must see "an end to all paramilitarism and activity and the putting beyond us, finally, of all paramilitary weapons". That was essential, he added.
"Acts of completion would also allow policing and justice to be devolved on a robust and workable basis, subject to the agreement between the parties," said Mr Ahern.
"Most importantly, acts of completion would allow the full potential of the agreement to be fostered and developed to the highest degree, with positive outcomes, tangible dividends and constructive opportunities for communities and individuals throughout the island of Ireland."
Mr Ahern said they wanted a police service representative of all sections of the community, supported by all sections of the community, and being held accountable by the chosen representatives of all sections of the community.
"People have to decide in their own democratic way how to address issues, but it is clear that the time has come when the new Police Service - and its officers now being recruited on an equal basis as Patten intended - are entitled to the support and co-operation of the entire community," he added.
The Taoiseach was speaking during a series of statements on the current situation in the North.
Mr Caoimhghín Ó Caoláin (SF, Cavan-Monaghan) urged the two governments to publish the joint declaration. "It should have been published last Thursday when my party colleagues and I, along with the other parties, were in Hillsborough," he added.
He said that while the joint declaration had not yet been published, there had been a quite unprecedented initiative by the IRA in which it had outlined to both governments its position in detail in an effort to move the process forward.
Critical issues remained, he said. "These include the transfer of power on policing and justice and the suspended status of the institutions and the absence of any clear commitment from the Ulster Unionist Party that it will work the institutions in a sustainable way," he added. "There is also the attempt to introduce sanctions against Sinn Féin, which are clearly outside the terms of the agreement. This is unacceptable."
The Fine Gael leader, Mr Enda Kenny, said he recognised the huge compromises which had already been made by the pro-agreement parties. "I commend Sinn Féin for their efforts in persuading the republican movement to enter the democratic process," he added.
"However, the time has now come for the IRA to play its part in creating the climate in which the peace process can be restored. The IRA must make it clear that their criminal activities will be ended and that the process of putting their weapons verifiably beyond use will be completed."
The Labour leader, Mr Pat Rabbitte, said the key to a long spell of democratic political activity lay in the hands of "P O'Neill, the mythical signatory of statements from the Provisional IRA". He added that the republican movement should now be the ones to take the final risk.
"We will, all of us, applaud the day that the entire republican movement has the vision and the foresight to say that democracy is the only way forward," he added.
