The Sinn Féin leader in calling on Micheál Martin to state if he has confidence in the Minister for Health.
Mary Lou McDonald has claimed the Fianna Fáil leader "is keeping Simon Harris in his job".
Her comments come as the controversy around the cost overruns at the National Children's Hospital continues.
Reports today suggest a memo is due to be brought before cabinet next week outlining some of the projects that may be postponed as a consequence of the overspend.
On Thursday, newly-published memos revealed Minister Harris knew of a likely €191m overrun in August last year - as well as a possible additional €200 million claim from a construction company.
He didn't inform the Government of the spiralling costs until November.
Minister Harris has defended his approach, saying he wanted a final figure before alerting other ministers.
Taoiseach Leo Varadkar has stated he still has 'absolute confidence' in the Health Minister.
Leo Varadkar said that even if Minister Harris had told him about the overruns earlier, he would have instructed him to do exactly what he did.
However, the controversy has led to claims from Sinn Féin that the minister's position is no longer tenable.
'Questions to answer'
Deputy McDonald insists the Fianna Fáil leader now needs to clarify whether he has confidence in Minister Harris.
Fianna Fáil remains in a confidence and supply arrangement with the Government, and the party hasn't called for the minister's resignation.
Speaking today, the Sinn Féin leader argued: "Given the public outcry, given the scandal around the children's hospital... it's only appropriate that Micheál Martin answers that question.
"Does he have confidence in Simon Harris - yes or no? Will he place a confidence motion himself in the Minister - yes or no? Will he support any motion that we might bring forward - yes or no?"
She said her party has already made clear that they have no confidence in the Health Minister.
Deputy McDonald added: "I have no difficulty moving a confidence motion, but we want to know it will succeed.
"It's Fianna Fáil not Sinn Féin that's keeping Simon Harris in office".
