Fianna Fáil has called on Minister for Justice Frances Fitzgerald to sack the Garda Commissioner.
Speaking on RTÉ's The Week in Politics, Fianna Fáil Justice Spokesperson Jim O'Callaghan said it would be in the best interests of the gardaí if Nóirín O'Sullivan was removed from office.
Mr O'Callaghan said the instinctive reaction within the gardaí to controversy is to pause it and to try to make things go away.
Fianna Fáil has also expressed "reducing confidence" in Tánaiste Frances Fitzgerald, with Mr O'Callaghan accusing her of failing to take political responsibility for the ongoing garda scandals.
However, Independent TD Clare Daly said that if Fianna Fáil really wanted the Garda Commissioner sacked they could make it happen but are failing to do so for narrow political reasons and fear it would trigger an election.
Minister of State Finian McGrath said he had absolute confidence in the Garda Commissioner.
Speaking before the Labour Party's annual James Connolly commemoration at Arbour Hill, leader Brendan Howlin said there are any number of grounds on which the commissioner could be asked to stand down.
He said there is a need for new senior garda management.
Mr Howlin also said the Tánaiste must provide leadership on policing or "inevitably there will be consequences for her".