Sinn Féin leader Mary Lou McDonald has said the Taoiseach should sack Minister Simon Coveney for his handling of the appointment of Katherine Zappone as a special envoy.
She warned that if Mr Martin does not take action by sanctioning Mr Coveney, her party would act.
Ms McDonald said this includes the possibility of tabling a Dáil no confidence motion in Mr Coveney.
Her comments come as the controversy over the appointment of Ms Zappone as a special envoy on freedom of expression continues.
The Government has rejected Opposition accusations of cronyism due to Ms Zappone’s previous role as an Independent minister in the last Fine Gael-led minority Government.
She was appointed to the job at a Cabinet meeting on July 27th but later declined the post amid the controversy that ensued.
Mr Coveney has denied that he effectively offered her the role before his officials carried out the work to create it and that Ms Zappone’s contacts with him amounted to lobbying for the job.
He told the Oireachtas Committee on Foreign Affairs Ms Zappone was mistaken in her belief that she had been offered the job last March.
Ms McDonald argued on Wednesday that the way the appointment was handled is behaviour that is “not of the standard that would be expected of any minister of Government”.
She added: “I know that the Taoiseach has said that Minister Coveney was wrong, that his behaviour was wrong.
“So the question now arises as to what the Taoiseach is going to do about this.”
She said Taoiseach Micheál Martin “needs to act” and “in the event that he is not prepared to act well then Sinn Féin will”.
Ms McDonald said the possibility of a no confidence motion is “on the table”.
Asked if she thinks Mr Martin should sack Mr Coveney she said: “I do” adding: “it’s very hard to see how the minister remains in his position given that we have had eight weeks of this controversy”.
‘Lacks any credibility’
She claimed Mr Coveney’s version of events “lacks any credibility whatsoever”.
Elsewhere, Fine Gael Minister for Higher Education Simon Harris defended Mr Coveney saying an "awful lot of information" has been provided on the appointment in recent days including four hours of testimony at the Oireachtas Committee and the release of documents by the Department of Foreign Affairs.
He said: “There’ll be some people no matter what Minister Coveney says who will not be satisfied. I think some of that is for political reasons.”
He added: “I think Minister Coveney has answered all the questions comprehensively, honestly, and he’s a person of integrity and I hope we can move on from this.”
Asked if he Coalition would collapse if the Taoiseach did remove Mr Coveney, Mr Harris said: “I really don’t think it arises. It’s not for me to speak for the Taoiseach... he spoke very comprehensively on this issue again last night through his spokesperson.
“There have been mistakes made here. There are lessons to be learned. Apologies have been issued.”
On Sinn Féin’s threat of a no confidence motion he said: “Am I in any way surprised that Sinn Féin may consider continuing to politicise this issue? No I’m not.”
He reiterated his defence of Mr Coveney saying he’s “honest”, “hardworking”, “person of integrity”.
He said “if Sinn Féin want to continue with the politics that’s their decision or their choice, but the government is getting on with the people’s business.”
Asked if it had been a mistake to approve Ms Zappone’s appointment at the July 27th Cabinet meeting, Mr Harris said: “Clearly now in light of what we know now - and we’ve all acknowledged that the process should have been handled differently - I think that appointment shouldn’t have gone ahead at that meeting.
“But just to be very clear. I’m a member of that Cabinet. It was a collective Cabinet decision.”
The Oireachtas Committee on Foreign Affairs is expected to invite Ms Zappone to answer questions about her appointment as an envoy and it is to discuss the possibility next week.
Mr Harris said it is "a matter for her" whether or not she attends adding: "She is a private citizen. She lives in the United States of America".