Fine Gael is to propose that all Dáil parties unite next week behind a motion calling on the IRA to decommission its weapons and end all criminal and paramilitary activity.
The party's Private Members Motion comes amid uncertainty within Government and Opposition parties about the state of the relationships between senior figures in the republican movement.
The Fine Gael leader, Mr Enda Kenny, said yesterday he was "concerned at the situation that appears to exist now, whereby apparently the leadership of Sinn Féin is either unwilling or unable to interpret the latest statement from the IRA".
He said on RTÉ's Morning Ireland programme that in the past such statements had been interpreted by Sinn Féin "with credibility, but that does not appear to be the case now and therefore I don't know what is actually happening within the republican movement. This is a source of some concern."
The Taoiseach also noted "the distancing of Sinn Féin comments from the IRA statements" in recent days. He did not elaborate on what significance he saw in this.
Fine Gael sources said they hoped to get support from the Government parties for their motion, and said they had deliberately excluded from it any criticism of the Government.
The motion calls on the Dáil to reaffirm that the Belfast Agreement must form the basis for any deal in the North; to note that all parties to the agreement undertook to pursue their political objectives by exclusively peaceful and democratic means; and that the agreement envisaged full decommissioning within two years.
It welcomes the Taoiseach's statement that the offer regarding the early release of the killers of Det Garda Jerry McCabe has been withdrawn; notes "the damage which has been done to the peace process by the robbery of the Northern Bank, and the assessment of the Irish and British governments that the Provisional IRA was responsible for this crime".
It also "notes with deep concern the recent comments by the Sinn Féin leadership regarding its interpretation of what constitutes criminality; views the recent statements issued by the Provisional IRA as a retrograde step and as an implicit threat to the Irish people; [ and] believes that a final, inclusive settlement must require that all paramilitary activity and criminality be brought to an end."
Finally, it calls on the republican movement "to clearly demonstrate its commitment to full decommissioning and to ending all its criminal and paramilitary activity".
Meanwhile, the Labour Party leader, Mr Pat Rabbitte, described last Wednesday's IRA statement as "834 words of petulance, self-pity, hectoring and general menace". Despite its length, it had failed anywhere to mention the Belfast Agreement, he said.
"Instead, there is an account of a peace process that has since 1994 been enhanced, developed and saved by a succession of 'significant', 'ambitious' and 'substantive' IRA initiatives, which have been attacked, devalued and dismissed by pro-unionists, anti-republicans and the British and Irish governments."
Mr Rabbitte said there had now been "a not very-thinly-veiled threat from the IRA when, it appears, they felt their first statement was not received with due respect and deference".
It was now "make your mind up time" for Mr Gerry Adams and Mr Martin McGuinness.
The Green Party leader, Mr Trevor Sargent, said the Taoiseach should consider recalling the National Forum for Peace and Reconciliation. All parties should "remain calm" following the two IRA statements this week.
"It is important to take stock of the peace dividend reduced paramilitary violence has brought in the last decade," he said. "If parties cannot work together, this is indeed serious. All can agree with the IRA statement on that point."
But he urged the IRA "to agree with the Green Party and almost every other party to the Good Friday agreement that the block to progress is the threat of violence and the capacity for violence. Much depends on Sinn Féin and the IRA ending the option of armed struggle.
"We are now on an unfortunate round of game playing with accusations, blame and counter blame clogging the airwaves. I am now calling on the Taoiseach and all parties to seriously consider recalling the National Forum for Peace and Reconciliation."