Roscommon-Galway TD Michael Fitzmaurice has quit the Independent Alliance grouping.
Deputy Fitzmaurice was the only member of the grouping not to vote for Enda Kenny as Taoiseach.
In a statement tonight, he said he felt he had to leave as his access to speaking time in the chamber while still in the grouping would be limited.
He said he will be voting with the minority Government on issues that benefit society at large, and wished his Independent Alliance colleagues "all the best".
Deputy Fitzmaurice said: "New rules on how the Dáil will operate will be published tomorrow and will detail how speaking time etc. will be allocated. I will endeavour over the coming days to join a technical group in order to get adequate speaking time in the Dáil in order to speak out for the people who elected me and give them a voice.
"It has become very clear to me in recent days, considering the criticism directed at some government TD's for expressing their opinions, that until the issues surrounding turf cutting are resolved and ordinary people are no longer criminalized for exercising their rights, that I could not be member of any government.
"To this end, I hope these matters can continue to be worked on and resolved for the betterment of all involved."
Deputy Fitzmaurice's stance on turf cutting on bogs was reported to have been one of the major points of contention during discussions between Independents and the Government ahead of the vote on Taoiseach earlier this month.
Independent Alliance co-founder Shane Ross has been appointed Transport Minister, while the group's Finian McGrath has been given the role of Super Junior Minister with Responsibility for Disabilities.