The prime minister was responding to cabinet minister Christopher Pyne's suggestion that legalising same-sex marriage is still on the agenda of some senior government MPs.
Speaking to reporters in Melbourne on Monday, Prime Minister Turnbull said there are "no plans" within the Liberal Party to change its policy on same-sex marriage.
"I can understand the frustration that the gay marriage is not resolved but the reason is has not been resolved is because of Bill Shorten," Prime Minister Turnbull said pointing to Labor's opposition in the senate.
"Our policy is clear, we have no plans to change it, full stop."
Defence Industry Minister Christopher Pyne made the comment to a gathering of moderate Liberals before the party's federal council meeting in Sydney last Friday night, News Corp columnist Andrew Bolt reported on Monday.
"Friends, we are in the winner's circle but we have to deliver a couple of things and one of those we've got to deliver before too long is marriage equality in this country," Mr Pyne said, according to a recording obtained by Bolt.
"And your friends in Canberra are working on that outcome.
"It might even be sooner than everyone thinks."
He also reportedly boasted about voting for Malcolm Turnbull in every federal Liberal leadership ballot.
Responding to the reports Tony Abbott accused Pyne of not being "fair dinkum" with the Australian people.
"This appears to be the confession that he has made to his close colleagues in the Left faction," Mr Abbott told 2GB radio on Monday morning.
"If you are a member of a Cabinet, you've got to be loyal and Christopher Pyne was not just a member of my Cabinet, he was actually in the leadership team and it is important that you show loyalty."
Mr Abbott added that it was "incredibly disappointing" to see Minister Pyne speaking out.
Prime Minister Malcolm Turnbull went to last year's election with Tony Abbott's plan for a plebiscite on same-sex marriage.
But the senate in November rejected legislation that would have allowed the national vote to take place, and same-sex marriage has been off the government's agenda since.
"It was a very clear policy that there would be no change without a plebiscite, and to dump the plebiscite, to do anything without a plebiscite would be a breach of faith with the people," Mr Abbott said.
Opposition Leader Bill Shorten said the Parliament should use its 20 sitting weeks of the year to "have a vote" on marriage equality.
"It would take five minutes for Malcolm Turnbull and I to go into parliament and put the issue to a vote," Mr Shorten said.
"Let's work together, people are sick and tired of the bickering going on in the parliament."
Deputy Prime Minister and Nationals leader Barnaby Joyce, who is in London, said he was focused on other issues, such as the trade mission he is about to undertake.
"I'm going to make sure that I'm concentrating on the issues that people who elected me want, which is to get the best return back through the farm gate," he told reporters after laying a wreath for London Bridge terror victims.
"What happens at dinners and other parts of Sydney is of no real consequence to me."