Foreign Affairs Minister and Cork South Central TD Simon Coveney has received the backing of the majority of the Dáil.
TDs voted confidence in Mr Coveney by 92 votes to 59.
Taoiseach Micheal Martin has accused Sinn Fein of tabling a motion of no confidence against Simon Coveney to get publicity and deliver "populist partisan attacks".
Opening the Government's motion of confidence in the Minister for Foreign Affairs, Mr Martin said there was "no question or debate" about the substantive issues in the Katherine Zappone controversy.
"They are uncontested," he said.
"The position involved was intended to be part-time and awarded no permanent benefits to anyone.
"There is no allegation of a benefit being sought for or conferred on any office holder, and ultimately as we know, no-one was appointed to the role.
"However, as I stress from the beginning, there is an important matter and it is a perfect perfectly legitimate issue of public concern.
Mr Martin added: "Some of the statements which Deputy (Mary Lou) McDonald has made in the past few days are genuinely breath-taking in their cynicism and the double standards involved.
"Deputy McDonald even went as far as to say yesterday that her party had been forced into putting down the motion because 'they were not prepared to look the other way'.
"Not prepared to look the other way? Sinn Fein?
"This debate simply isn't long enough for us to go through the list of dramatically worse and often sinister events where looking the other way has been the defining essence of the Sinn Fein response."
Green Party leader Eamon Ryan expressed his backing for Mr Coveney, describing him in politics as "tough, gruelling but fair, knowledgeable, committed and sincere in all the dealings that I have had with him".
He added that Brexit has proven "what a capable foreign minister he has been and is at this present time".
Sinn Fein president Mary-Lou McDonald, whose party moved the no-confidence motion against Simon Coveney, said they were acting against "the culture of cronyism at the very heart of this government".
She said the motion was brought "because the Taoiseach refuses to do his job, he refuses to hold Minister Simon Coveney to account".
Ms McDonald claimed Mr Coveney "sought to make up a job for a friend and a former colleague, and when caught red-handed he went about covering his tracks".
"This is by any standard an abuse of office and Sinn Fein was left with no option but to move a no-confidence motion," she said.
She accused Fianna Fail, Fine Gael and the Green Party "to cast this fiasco as a non-issue".
Mary-Lou McDonald said the issue "goes to the heart of how politics has been conducted in this state for decades".
"Gentlemen, it must end here tonight because this generation wants and deserves far better," she said.
"I say to all of you who line up in defence of cronyism, you might delay change but you will not stop it. The days of the Fianna Fail/Fine Gael cosy club are numbered."
Taoiseach Micheal Martin said he wishes Marc Macsherry well.
In a statement, the Fianna Fail leader said: "The Taoiseach regrets the resignation and wishes Marc well."
Fianna Fail TD Mr MacSharry resigned from the parliamentary party ahead of a no-confidence vote in the Minister for Foreign Affairs.
Tanaiste Leo Varadkar accused Sinn Fein of attempting to "hound a decent man out of office for cheap publicity".
He said it was an "honour to express my full confidence in my friend and colleague Simon Coveney", adding he "knows nobody more committed to public service than he".
Mr Varadkar said Mr Coveney "made mistakes when it came to the appointment of Katherine Zappone as special envoy".
"He and I have acknowledged and apologised for our mistakes in that regard," he said.
However he stressed "the need for balance", paying tribute to Mr Coveney's work on the New Decade New Approach deal in January 2020 which led to the restoration of the Stormont Assembly.
"Without him, Michelle O'Neill would not be the deputy First Minister today and there would not be an Executive in Northern Ireland, he put back together the Executive Sinn Fein collapsed in a tactical act of arrogance leaving Northern Ireland without a voice for three years during the Brexit negotiations," he said.
"Sinn Fein knows the work that he put in to ensure there was no hard border in Ireland yet they seek tonight to hound an honourable man out of office for cheap publicity and political gain."
Simon Coveney has said he "should have and could have dealt with" controversy around the appointment of Katherine Zappone as a special envoy "much more comprehensively in early August".
Speaking in the Dail as TDs debated confidence in him, Mr Coveney said he had not taken the issue seriously enough and was "too defensive" in interviews.
"I allowed speculation to drift into a political narrative that does not reflect the truth of what actually happened," he said.
"I regret this issue has distracted from the important work that we've been trying to do and for the mistake made by me in advance of the cabinet decision, and subsequently in terms of not clearing these issues up earlier.
"I've apologised to the Taoiseach and my colleagues, and I do so again this evening to everybody in this house."
Mr Coveney defended his decision to appoint Katherine Zappone as a special envoy "following an extensive process, was in no way corrupt or dishonest".
"It was a genuine effort to add to the credibility and effectiveness of Ireland in an area of promoting human rights and freedom of expression," he said.
"This is one of many special envoy roles that Ireland has appointed, government after government, and was absolutely consistent with what many other like-minded countries are currently doing."
He said his department is undertaking a full review of how special envoys are appointed.
Mr Coveney said in 23 years in politics, he made mistakes but that he has never had his integrity questioned "in the way that it has been in the last month leading to this debate".
He blasted the no confidence motion as a "political tactic and to try and extend a political controversy, and to reinforce a false narrative of cronyism to damage relations in this government".
"Sinn Fein are doing what they do so often, north and south, stoking tension with an exaggerated narrative in an effort to create anger, resentment and division, not just in this House or in government but across society more generally," he said.
"I sincerely hope that following this motion this evening I can return to focusing fully on the important work of government and the office that I am privileged to hold."