Sinn Féin is to publish a motion of no confidence in the Health Minister Simon Harris.
Party leader Mary Lou McDonald confirmed the move on Twitter.
This morning we publish a motion of no confidence in health minister Simon Harris.
— Mary Lou McDonald (@MaryLouMcDonald) February 11, 2019
A party spokesperson said: "Apologising and correcting the record of the Dáil is all very well but it is no substitute for political accountability.
"We have to have political accountability for this gross mismanagement of our public finances which will have a knock on affect on other capital projects across the State.
"Simon Harris misled the Dáil, he misled his government colleagues during crucial budget negotiations, he misled Fianna Fáil during negotiations on the renewal of confidence and supply and, most seriously, he misled the public.
"His position is untenable and Sinn Féin will table a motion of no confidence in him."
Mr Harris is set to apologise in the Dáil in the coming days for not providing additional information about the new national children's hospital budget when asked in September.
Answering a parliamentary question, Minister Harris told Fianna Fáil's Barry Cowen on September 18th that spending to that date was "in line with the expected expenditure profile" and the budget for the project remained just over €1bn.
Deputy Cowen had asked whether there had been an overspend on the project.
On Thursday, newly-published memos revealed Minister Harris knew of a likely €191m overrun in August last year - as well as a possible additional €200m claim from a construction company.
Minister Harris ultimately informed the Government of a €450m overspend in November.
It is now believed the project will cost at least €1.7bn.
The motion will read: "This House, declares that Dáil Éireann has no confidence in the Minister of Health Simon Harris, and calls on him to resign from his ministerial position forthwith."