A spokesperson for the Taoiseach said Micheál Martin does have confidence in Minister for Foreign Affairs Simon Coveney.
The comment comes after the Sinn Féin leader earlier called on the Taoiseach to sack Mr Coveney over what she branded behaviour not of the standard expected of a minister.
Mary Lou McDonald said if Micheál Martin failed to act, then Sinn Féin would.
She said this would include the option of a no-confidence motion in the minister, which is on the table.
Asked again if the party would table that no-confidence motion, she said: "It could come to that."
It comes as Mr Coveney faces sustained pressure over the proposed appointment of former ministerial colleague Katherine Zappone to a UN special envoy position.
The leader of Sinn Féin has called on the Taoiseach to sack Minister Simon Coveney over what she branded behaviour 'not of the standard expected of a minister.'— RTÉ News (@rtenews) September 8, 2021
Mary Lou McDonald said if Micheál Martin failed to act then Sinn Féin would | Read more: https://t.co/Ksh2ovnQpy pic.twitter.com/hxBi0jFxOw
At an Oireachtas Committee yesterday, Mr Coveney apologised over what he described as the "political fiasco" surrounding the appointment.
He has maintained that Ms Zappone did not lobby him for the job and said that he had to address the committee twice in as many weeks due to the "sloppiness" of some of his answers on the first occasion.
Sinn Féin yesterday raised the prospect of a no-confidence motion in the Dáil against Mr Coveney, and the minister has been criticised by coalition partners in Fianna Fáil.
Earlier, Minister for Finance Paschal Donohoe said he suggested towards the end of last year that Ms Zappone "have a chat" with Mr Coveney to get his advice on things.
Minister Donohoe said that Ms Zappone was thinking about her future at that point, as she had been in the US for a little while.
"I then said to Simon that Katherine was going to give him a call and that was it. That was the sum total of my involvement in this," the minister said during a webinar organised by the farming and agribusiness advisory firm, IFAC.
He insisted that Ms Zappone had not canvassed him for a job. "She didn't lobby me. It was a very general discussion," he said.
Minister Donohoe said there is likely to be greater clarity for ministers around how they use their phones and how they contact each other in the aftermath of the controversy.
Fianna Fáil TD Jim O'Callaghan said senior Fine Gael ministers need to show more respect for the Taoiseach's office and their coalition partners, warning that "if they keep going on doing business like this, we won't do business for long".
Speaking on RTÉ's Today with Claire Byrne, Mr O'Callaghan said the ongoing controversy over the UN special envoy role showed very "casual and cavalier behaviour" by Fine Gael ministers that displays "an extraordinary lack of respect for Fianna Fáil and the Green Party".
He called it "a Fine-Gael omnishambles" that has inflicted a lot of damage, and said the responsibility rests with senior people in Fine Gael, who need to keep their coalition colleagues informed of important developments and "cannot blindside the Taoiseach".
Mr O'Callaghan said it would be very helpful if Ms Zappone appeared before the Oireachtas Committee on Foreign Affairs.
He said that while this is not necessarily "a sacking issue" for Minister Coveney, the Taoiseach could perhaps remove his powers to appoint special envoys in the future.
Jim O'Callaghan describes the short-lived Katherine Zappone appointment as "cronyism."— Mícheál Lehane (@MichealLehane) September 8, 2021
Sinn Féin's Donnchadh Ó Laoghaire also said he thinks Ms Zappone should appear before the committee.
Speaking on RTÉ's Morning Ireland, he said the country needs to hear from the Taoiseach that he believes Mr Coveney's account of events surrounding the appointment of Ms Zappone.
"Does he believe Simon Coveney? Because I don't think that the public does.
"I think it's unbelievable. I think it's ludicrous," Mr Ó Laoghaire said.
Green Party leader and Minister for the Environment Eamon Ryan said he supports Mr Coveney and said he thinks it is time for the Government to move on and deal with the serious issues facing the country.
Speaking on his way into Cabinet, Mr Ryan said he watched most of the committee hearing yesterday and he thinks all of the information has come out and does not expect there will be any more developments.
Mr Coveney said Ms Zappone did not ask him for a job at any stage, but did text him for advice in February about the possibility of working with the United States Agency for International Development (USAID) on women, gender equality and LGBTQ issues.
In a statement yesterday evening, Mr Martin said the minister had given his account of what happened, but that being said, lessons need to be learned by Government on the handling of the issue.