A senior Fianna Fáil TD said the controversy surrounding Katherine 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, which has been rolling on for some seven weeks.
He stopped short of calling for Micheál Martin to sack Simon Coveney, but said the Taoiseach has the constitutional right to remove a minister.
On Tuesday, the Minister for Foreign Affairs apologised 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 Government.
"We have seen very casual, inappropriate and disrespectful behaviour by certain senior Fine Gael ministers," Mr O'Callaghan told RTÉ.
"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.
Mr Coveney appeared before an Oireachtas committee for a second time on Tuesday, in which he gave further evidence about the appointment process.
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.
However, Mr O'Callaghan said that sacking a minister should not be the first port of call for ministerial wrongdoing or ministerial incompetence.
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.