Two Cabinet ministers have called for HSE boss Tony O'Brien to step aside.
Katherine Zappone and Finian McGrath told their ministerial colleagues it was their personal view that he should go.
However, they will vote with the Government and against a Sinn Féin motion of no confidence next week.
The party's motion won't go ahead this evening because of a procedural issue in the Dáil.
However Sinn Fein's Health Spokesperson Louise O’Reilly says the party will bring it forward next Tuesday instead.
She explained: "We need to talk about accountability - there is no accountability in the HSE for as long as Tony O'Brien remains as head of that organisation.
"There can be no accountability until the victims' voices are heard - they are calling for Tony O'Brien to be stood down, and we are back that call."
Mr O'Brien is due to finish up in his role this summer, having announced his intention to do so before the cervical scandal began.
