Sinn Féin says criminals masquerading as Republicans must cease all activity.
The statement comes after the Justice Minister ordered out a new assessment of the status of the Provisional IRA - in the wake of the murder of Kevin McGuigan.
Sinn Féin says the review will show that the IRA no longer exists, and the party is welcoming the assessment.
Laois Offaly TD Brian Stanley is calling on dissidents to give themselves up to the authorities
The Justice Minister Frances Fitzgerald has asked the Garda Commissioner to liaise with the PSNI, and carry out a fresh assessment of the status of Provional IRA.
She also says the parties in the North should get on with their work, and allow the PSNI investigation into the killing of Kevin McGuigan to proceed.
Last week, PSNI chief George Hamilton said elements of the IRA were responsible for the murder of Mr McGuigan in Belfast.
Sinn Féin have vehemently denied the claim that the IRA is still in existence - with party president Gerry Adams making firm denials that the group is still operating.
In a statement released this afternoon, Mr Stanley also attacked Joan Burton, saying "the Tánaiste would rather focus on an imagined IRA than deal with the real issues facing people," and is using the IRA issue to deflect from the upcoming planned mass protest against water charges.
“The reality is that the organisation the Joan Burton refers to no longer exists," Mr Stanley said.
“With the Labour Party support decimated in the opinion polls it is no surprise that both their leader and deputy leader have attacked Sinn Féin this week in a cynical and self-serving way.
“Sinn Féin has repeatedly said that anyone with information about criminality should bring that to the PSNI or the Gardaí," he added.