The issue is expected to be raised at party-room meetings when Parliament returns next week.
Turnbull had supported a nationwide vote on the issue, called a plebiscite, before any legislation could be introduced into parliament, but now seems to be backing off that requirement.
“In our party, backbenchers have always had the right to cross the floor,” Turnbull told reporters. “In the Labor Party you get expelled for doing that, but it has always been a fundamental principle in the Liberal Party and indeed the National Party.”
Proponents of marriage equality have opposed the plebiscite, saying the campaigning against it could cause depression rates and suicide attempts among LGBT youth to rise sharply.
“It’s in our best interests to move on from this issue so we can focus on the sorts of things I think people voted for me and for my party to deal with — tax reform, fixing the budget, national security,” said Liberal backbencher Tim Wilson.
Openly gay Federal Liberal MP Trevor Evans said he plans to raise the issue next week, calling it the quickest and most efficient way to deal with the matter.
Four Liberal MPs would be needed to cross the aisle to join forces with the Labor Party to interrupt the scheduled business of Parliament and force a vote on the marriage equality legislation. If put to a vote in Parliament, the bill is expected to easily pass.