Earlier, Leo Varadkar and Simon Coveney warned that Fine Gael needs to prepare for an election
The Government has survived a confidence motion in itself in the Dáil this evening.
The final result of the vote was 57 to 52. Fianna Fáil abstained from voting.
The motion passed with the backing of the Independent Alliance - who agreed to support Fine Gael after 'considering' withdrawing from the minority government over ministers' handling of the Maurice McCabe controversy.
Earlier, the two leading candidates to replace Enda Kenny as Fine Gael leader and Taoiseach warned the party needs to prepare for an election.
Enda Kenny addressed his parliamentary party this evening, acknowledging the past week had not been easy.
However, as expected, he made no mention of the leadership.
There were calls for unity and a rallying of the troops, but then Leo Varadkar - the Social Protection Minister and one of the leading contenders to succeed Mr Kenny - called for a special parliamentary party meeting next week to begin preparations for an election.
The other contender for the throne, Simon Coveney, added his voice to the need for readiness sooner rather than later - although stressed they need to be united.
At the start of the Dáil debate on the confidence motion, Mr Kenny offered the Garda whistleblower Sergeant Maurice McCabe an apology for the way he has been treated.
Cabinet has agreed to a public inquiry into an alleged smear campaign against Sgt McCabe. Reports last week revealed that he had faced a false allegation of sexual abuse.
"I offer a full apology to Maurice McCabe and his family for the treatment meted out to them, as exposed in recent programmes," Enda Kenny hold deputies.
Fianna Fáil abstained from the vote tonight as part of the confidence & supply agreement with Fine Gael.
However, party leader Micheál Martin warned that the agreement has been put under "serious strain":
Opposing the motion of confidence, Sinn Féin's Gerry Adams argued: “Whistleblowers - brave citizens - have been the target of systematic campaigns of abuse and harassment from within An Garda Síochána.
“In no other modern State would such actions be tolerated. Yet, under the watch of two parties that have dominated politics here since partition this is the state we are in."
He added: “Between them, Fine Gael and particularly Fianna Fáil have been responsible for a culture of insiderism, strokes, cronyism, corruption, graft, cute-hoorism, brown envelopes, digouts and whatever you’re having yourself."
Earlier, the Independent Alliance and the Taoiseach met over the handling of the Maurice McCabe affair.
The alliance has said its continued participation in Government "will be conditioned on a comprehensive resolution of what are by any standards extremely worrying allegations of malpractice within areas of An Garda Síochana" in relation to Sergeant McCabe and other Garda whistleblowers.
Minister Shane Ross said they have gained an agreement from the Minister of Justice for a 'thorough investigation' into the force, led by an international policing expert.
He said the group has serious concerns about the ongoing difficulties in the Garda sector, and wants them investigated.
The Transport Minister also said the alliance had been "dismayed and frankly disturbed by contradictory versions of events which had emerged this week".
"Some aspects of Cabinet communication are not working effectively, or appropriately," he argued. "This is not how we want to do business."
Minister Ross added that his group had "considered" withdrawing from Government over the issue.
Meanwhile, the Social Protection Minister told the Dáil tonight that Sergeant McCabe is a hero and is owed an apology by the Government.
Leo Varadkar used his time on the debate of confidence in the Government to claim that Maurice McCabe has been subjected to a "scurrilous" campaign to discredit him and that the inquiry must find out who was involved and who organised it.
Minister Varadkar said: "Tonight, I call on all those with information to come forward. In particular, I call on individual Gardaí who spread rumours, passed to them by superiors, perhaps believing them to be true, to come forward and offer to give evidence to the public inquiry. They too were deceived and are not to blame."
He acknowledged that the events of the past week have damaged Fine Gael - but the party can and will put things right.