The Taoiseach has called on Mary Lou McDonald to fully explain her relationship with Jonathan Dowdall, claiming Sinn Féin had "more than an inkling" about the former party councillor's background.
Leo Varadkar has also suggested that Ms McDonald return a €1,000 donation made to the party by Mr Dowdall.
He told the Dáil that the Hutch verdict highlights the importance of the Special Criminal Court and called on Sinn Féin to support its continuation.
"I call on Sinn Féin, on the leader of Sinn Féin in particular, to affirm that they will vote for the renewal of the Special Criminal Court in June, not have an abstention, not a case of not turning up, but that they will vote for the retention of the Special Criminal Court.
“I think the fact that there was one acquittal, even though it was not the outcome that the State desired does confirm that the Special Criminal Court is a place where people get a fair trial, and the beyond reasonable doubt principle applies,” Mr Varadkar said.
He added: "I believe it is also important that the €1,000 donation should be returned, that information be disclosed on other donations made by Mr Dowdall to Sinn Féin and that we get more detail on Sinn Féin's knowledge of Mr Dowdall's actions."
Mr Varadkar who previously described Dowdall as a "friend" of Ms McDonald and "somebody who would have been one of her cronies" said it was “clear” from a radio interview with Sinn Féin TD Eoin Ó Broin on Tuesday morning that there was more “than an inkling” of Mr Dowdall’s activities.
Mr Ó Broin said the party made it “very clear” that Mr Dowdall should have never been a member of Sinn Féin and that had the party known about his activities, he would have been nowhere near it.
“There are many individuals and organisations who had relationships with Jonathan Dowdall that had no inkling that he was involved in this kind of criminality,” he said.
Speaking to RTÉ’s Morning Ireland, Mr Ó’Broin said Sinn Féin officials did not question Mr Dowdall about allegations of criminal behaviour in the run-up to the 2014 local elections.
“This is one of a number of lies that Jonathan Dowdall clearly put forward,” he said.
Speaking at Leader’s Questions, the Taoiseach said there is a “clear and ongoing link” between republican paramilitaries and organised criminal gangs.
“These are similar people who commit similar crimes, it was always thus they are not worlds apart in fact they inhabit the same netherworld in my view,” he said.
Mr Varadkar said he did not think “in any way” that Sinn Féin was responsible for John Dowdall’s activities. However he called on the party to disclose knowledge of his actions.
“I don’t believe in guilt by association," he told the Dáil.