Reform Alliance TD Lucinda Creighton says she has "reservations" about gay marriage.
Ms Creighton said she was in favour of holding a referendum on gay marriage, but declined to say if she would support it.
"I have reservations," she said.
Ms Creighton says there needs to be a debate about what equality means, including a variety of rights and treatment under the tax laws.
"Whether that involves changing the definition of marriage is part of that debate - not the only part," she said on RTE's Marian Finucane Show.
Fine Gael is committed to holding a gay marriage referendum, but the party has yet to form a policy on the issue.
Taoiseach Enda Kenny has repeatedly refused to state his position.
The Reform Alliance has been accused of being conservative.
The group was formed following the expulsion of Fine Gael TDs and Senators from the parliamentary party for voting against the abortion legislation.
Ms Creighton's comments follow her colleague Fidelma Healy-Eames opposition to gay adoption.
"Personally I have an open mind on the issue of gay marriage. However, gay adoption raises a number of concerns in relation to how we rear children and the dangers of commodifying children," she wrote in the Sunday Business Post before Christmas.