The Taoiseach has said Gerry Adams must accept his responsibilities as Sinn Féin leader to help bring criminals to justice.
Enda Kenny's comments came after Deputy Adams insisted his party answered only to the electorate - and not to the IRA Army Council.
"We're not accountable to any other group or organisation," he said.
But the Taoiseach said Deputy Adams has to do more - and questioned his claims about a link between Sinn Fein and the IRA.
Mr Adams told the Dáil his party is not run by the IRA army council and his party is responsible to only one group - the Irish electorate.
Dáil proceedings were today dominated by the PSNI assessment that the IRA army council exists, and that members of the IRA believe the Army Council also governs Sinn Féin.
Mr Adams says Sinn Féin members have risked their lives by committing themselves to peace, and says the claims by British security forces are simply not true.
While the Director of Public Prosecutions in Northern Ireland is calling for an investigation into claims security forces colluded in at least 24 murders.
It is claimed double agents within the IRA were allowed to commit crimes to gain the trust of gunmen.
Two investigations will centre on Stakeknife - the codename for a high-ranking army agent within the republican organisation.
A report yesterday by the PSNI and MI5 claimed the IRA still maintains an army council, and has control over Sinn Féin.
The report said the group is committed to the peace process - but individual members are engaged in criminal activity including smuggling.
The British government-ordered review into paramilitary structures in Northern Ireland found parts of the Provisional IRA still exist in a "much reduced form".
The report described the Provisional IRA as being "committed to achieving a united Ireland by political means", adding: "The PIRA of the Troubles era is well beyond recall".
The Northern Ireland Secretary, Theresa Villiers, is calling for paramilitary organisations to be monitored and gradually phased out.
But speaking on Newstalk Breakfast, she refused to say whether or not she knows who is on the IRA army council.
Sinn Fein TD for Donegal-North East, Pádraig Mac Lochlainn, says republicanism has moved on.
Meanwhile former Taoiseach Bertie Ahern told the Pat Kenny Show here on Newstalk the issues will continue to affect Stormont until they are finally resolved.