Senior Liberal senator Arthur Sinodinos says his party should allow a conscience vote on same-sex marriage.

Senator Sinodinos has previously declared his support for marriage equality, despite his party officially opposing a push to change the Marriage Act in the last parliament.

He said the Liberal Party should allow senators and MPs to vote as they like.

“I think we should [be allowed a conscience vote], I think you’ll get a truer test of the feeling within the parliament if both the big parties of politics, the Coalition … [and] the Labor Party do have a conscience vote,” he told Sky News.

“I think that will make for a more interesting debate and a truer test of the feeling within the parliament on this subject.”

In 2013 as opposition leader, Tony Abbott said the issue of whether to allow members a free vote in Parliament would be a “matter for the post-election party room”.

The issue was not discussed in March at the last party room meeting before the budget.

“Tony Abbott indicated at the beginning of this parliament that while our policy was that marriage is between a man and a woman, it was up to the party room ultimately to decide whether there should be a conscience vote,” Senator Sinodinos said.

“I think at some stage it’s inevitable there will be a call on this [within the Liberal Party].”

Meanwhile, Labor frontbencher David Feeney has rejected a call for the ALP to have a binding vote on same-sex marriage.

The party’s official policy is to support marriage equality, but it allows a conscience vote on the issue when it is before Parliament.

Deputy leader Tanya Plibersek wants to change that and compel colleagues to vote for same-sex marriage.

Mr Feeney has told Sky News he supported marriage equality, but not a binding vote.

“I don’t think the challenge is for Labor to engage in coercing people to support this legislation,” Mr Feeney said.

“I think the challenge is for supporters of marriage equality, and I’m one of those, to actually engage in the debate and persuade the unpersuaded.

“It’s pretty messy for Labor to insist that the Coalition have a conscience vote while at the same time proposing to abandon our own conscience vote.

“I think the conscience vote is the right mechanism for us to advance this issue on both sides of the Parliament.”

Ms Plibersek spoke publicly on the issue as acting leader when opposition leader Bill Shorten was out of the country last week.

She is set to push the issue at Labor’s National Conference in Melbourne in July.