It is "not rocket science" to bring an end to paramilitarism, criminality and decommissioning of weapons, the Taoiseach told the Dáil.
Mr Ahern welcomed comments by Sinn Féin's leader in the House, Mr Caoimhghín Ó Caoláin renouncing criminality of any kind, but he said that "we need deeds as well as words".
Sinn Féin "will understand if we reserve judgment. Its members have to accept that their words cannot easily be accepted at face value."
He was not interested in arguing about Sinn Féin's mandate or demonising it, but he said that "we want no ambiguity, no fudge and no messing. Let us be straight, and let us get to the bottom line".
The Taoiseach also insisted there were no differences whatsoever between himself and the Minister for Justice, Mr McDowell on the peace process, that Mr McDowell got detailed security briefings daily, while he received occasional and less-detailed briefings.
He dissociated himself "totally, from any derogatory remarks" about the Minister by any Fianna Fáil councillor and said the Government was of "one mind" about the process.
He agreed, however, with Fine Gael leader, Mr Enda Kenny that who was, or was not, on the IRA army council was a "sideshow" from the main matter in the peace process. "The broad issue is that the leadership of Sinn Féin and the IRA are extremely close."
Mr Kenny had asked if there was a "split" in the Government over remarks by a Fianna Fáil councillor, who in a radio interview, called for Mr McDowell's resignation.
The Taoiseach said that "I dissociate myself totally from any derogatory remarks about the Minister for Justice, made by any Fianna Fáil councillor".
It was obvious, he added, that the councillor "does not know what she is talking about".
In the Dáil on Tuesday, Mr Ó Caoláin had rejected criminality of any kind and said that no republican worthy of the name could be involved in criminality.
People in the party involved in criminal acts should leave their ranks immediately, the Sinn Féin deputy had also stated.
Mr Ahern said yesterday, however, "we all know what must be done. We all know what we want Sinn Féin and the IRA to do. Their actions have to be capable of being understood in clear terms by the people of this island."
They wanted an end to paramilitary and criminal activity by the IRA and the decommissioning of IRA arms, and would not be able to restart the process if that was not achieved.
"In effect, large amounts of money are being hauled around the Republic of Ireland by various people. It is being laundered for the Provisional IRA."
Mr Kenny had said that the row over who was in the IRA was a sideshow and an "unwarranted distraction" from the main issue of the "web of criminality" which "seems to reach right to the inner sanctums of Irish business, and which affects the economy and goes to the heart of our democratic system". The Taoiseach said that the "fundamental issue" was putting arms beyond use, the issue of criminality and the end of paramilitarism.
Labour leader, Mr Pat Rabbitte, was fearful that "we will drift back into a position whereby we do not exclude for the sake of not doing so, and engage in the same creative ambiguity and confusion as before".
Mr Ahern agreed that there was an opportunity to bring this phase of the peace process to an end. "We have brought other parts to an end. Let us not forget that."