The Taoiseach has welcomed Sinn Féin's vow to banish criminality from its party but Mr Ahern urged them to match their words with deeds.
Mr Ahern told the Dáil: "We're listening very closely to what Sinn Fein is saying.
"Those words cannot simply be accepted at face value. We want no ambiguity, no fudge, no messing."
The Taoiseach, Mr Ahern
Sinn Féin's leader in the Dáil, Mr Caoimhghin O Caolain yesterday made a clear statement saying the party would banish rogue members from its ranks and reaffirmed a commitment to disbanding the IRA and implementing the Belfast Agreement.
Mr Ó Caoláin refused to admit if his ultimatum was a significant shift in the party's position in relation to its alleged links with criminality.
Speaking later on RTE's Primetimelast night, Mr Ó Caoláin reiterated an the Dáil statement that activists engaged in criminal activities outside the legitimate political norm "should leave the party today".
He said of his Dáil statement: "I certainly intended it to be as clear and as unambiguous as I could possible deliver.
"It is addressing many audiences but I hope that not only all of the elected opinion represented in Leinster House, but indeed republican opinion the length and breadth of the island will take note of what I have said.
"I've made it clear today. I've made it clear and clearer I believe than I've ever done before that we're working towards an end to the Irish Republican Army."
"All of the years of hard work leading up to the Good Friday Agreement and since has created great frustration for the Sinn Fein leadership, as much and perhaps more than any other opinion on this island and we want to see a conclusion to all of this reached and reached speedily."
The Taoiseach also agreed with a question by Labour party leader, Mr Pat Rabbitte, that Sinn Fein and the IRA should "turn in the killers" of Belfast man Robert McCartney, murdered in a pub row over three weeks ago.