The party says it wants to hear further from Noirín O'Sullivan when she appears before the Oireachtas Committee on Thursday.
It also says Tánaiste and Justice Minister Frances Fitzgerald needs to answer questions in the Dáil after five days of silence.
The Labour Parliamentary Party is considering a Dáil motion that would involve major change in senior Garda management.
Party leader Brendan Howlin says he's of the belief Noirín O'Sullivan – and others – should go.
