This comes after Liberal MP Cory Bernardi criticised Communications Minister Malcolm Turnbull for his public support for same-sex marriage, which included comments at the weekend arguing that Australia was out of step with jurisdictions in the US, New Zealand, Canada and South Africa.

The controversial South Australian senator urged Mr Turnbull on Monday to either resign from the frontbench or stop commenting on ''fringe issues outside party policy''.

West Australian Liberal MP Dennis Jensen also said Mr Turnbull's comments on gay marriage were ''unhelpful'' and not befitting a cabinet minister.

But on Tuesday, Mr Abbott moved to hose down acrimony within his Liberal team.

''All of us cop a bit of flak from time to time, including sometimes from people in our own party,'' he said.

''The gentlemen in question have well-known views on this subject. The Liberal Party is a broad church, always has been, always will be.''

Mr Abbott said he was friends with both Mr Turnbull and Senator Bernardi, but gave no sign of softening his personal opposition to same-sex marriage.

''Everyone knows that I take a fairly traditional position on that particular subject, but I understand that not everyone shares my view,'' he said.

The Prime Minister repeated his comment that it would be up to the party room to decide whether Liberal MPs should get a conscience vote on the matter.

''If this matter were to come before the new parliament it would be dealt with by our party room in the usual way,'' he said.

At the weekend, Deputy Labor leader Tanya Plibersek said she would introduce a private members bill on same-sex marriage and was looking for a Liberal MP, namely Mr Turnbull to co-sponsor it.

Ms Plibersek said she would introduce the bill only if Coalition MPs were given a conscience vote.