The leader of Sinn Féin has said the Taoiseach must sack Simon Coveney or else the minister could face a no-confidence motion.
Mary Lou McDonald said that Mr Coveney's handling of the Katherine Zappone crisis is "not the standard expected" of a government minister.
The Dublin TD called for Micheál Martin to sanction the Foreign Affairs Minister, or Sinn Féin would consider tabling a motion of no-confidence in the Fine Gael minister.
It comes a day after Mr Coveney apologised to an Oireachtas committee for his "sloppiness" in addressing answers about the appointment of Ms Zappone to a UN role, admitting that it has caused a "political embarrassment" for the Government.
His assertion that Ms Zappone mistakenly believed she had been offered the job in March, months before Cabinet was made aware, has been widely criticised.
Ms McDonald said: "Eight weeks into this crisis, Mr Coveney sticks to a version of events that is wholly incredible. He continues to deny that there was any job offer made on March 4.
"The question now arises is what is the Taoiseach going to do about it.
"There needs to be accountability and appropriate sanction for Simon Coveney, the Taoiseach needs to act today and set out very clearly what sanction he proposes to take.
"It's hard to see how Minister Coveney can stay on given all that has transpired in the last eight weeks and given the fact that so far he sticks to a version of events that lacks any credibility. Nobody believes the version of events that has been set out by Minister Coveney."
Ms McDonald told reporters she believes he should be sacked.
"If the Taoiseach fails to act or creates some kind of alibi that he is the Taoiseach, but only for Fianna Fail ministers, which is wholly ludicrous, then of course we will take action and the possibility of a no-confidence sanction is on the table."
It comes after as a senior Fianna Fail TD said the controversy surrounding Ms Zappone was an "omnishambles of Fine Gael's creation".
Jim O'Callaghan said it has inflicted a lot of damage, and that it is a story about Fine Gael's failure.
The Dublin TD accused a number of senior Fine Gael ministers of being "inappropriate and disrespectful" in their handling of the controversy.
He stopped short of calling for his party leader to sack Simon Coveney, but said the Taoiseach has the constitutional right to remove a minister.
"We have seen very casual, inappropriate and disrespectful behaviour by certain senior Fine Gael ministers," Mr O'Callaghan told RTÉ.
"We need to recognise a responsibility for this rests with Fine Gael, and the people at senior levels in Fine Gael need to recognise that they can't operate in the silo, they have to keep their coalition colleagues informed of important developments, they can't blindside the Taoiseach.
"It was an omnishambles of Fine Gael's creation.
"They can't be disrespectful to the Taoiseach the way it happened in the past, but we now need to ensure that this doesn't happen again."
The Government has been under pressure in recent weeks over the controversy surrounding the abandoned appointment of Ms Zappone as UN special envoy on freedom of expression.
The former children's minister stepped back from the position after a storm arose around the manner of her appointment.
However, Mr O'Callaghan said that sacking a minister should not be the first port of call for ministerial wrongdoing or ministerial incompetence.
"This type of cavalier, casual method of doing business by Fine Gael has to stop, because to quote Mr (Leo) Varadkar, if they keep going on doing business like this, we won't be doing business for long," Mr O'Callaghan added.
Asked whether he believed what happened was cronyism, he replied, "yes".
He also said it would be helpful if Ms Zappone appeared before the Oireachtas committee.
Speaking ahead of Fianna Fail's two-day parliamentary party think-in on Thursday, Mr O'Callaghan denied he is among a number of elected members who would back a no-confidence motion against his party leader.
Mr O'Callaghan said there is concern in the party of how it is performing in the polls, adding that they cannot hide from the election results.
"My own view is that, at present, a lot of people don't know any more what Fianna Fail stands for, and I think we need to be much clearer with them in terms of what we stand for," he added.