Liberal MPs will be allowed a “very full, frank and candid and decent” debate about legalising same-sex marriage, Tony Abbott has promised.

The prime minister was responding to a Labor move to introduce a private bill to parliament next week with a likely vote later in the year.

Abbott indicated a debate about giving Liberal MPs a conscience vote on the issue was not a priority at this stage.

However, that’s likely to change the closer parliament comes to voting on any legislation.

“I’m sure at that time we’d have a very full and frank and candid and decent debate inside the party room,” he told reporters in Canberra on Wednesday.

Abbott acknowledged there were differing views in the Liberal party and closer to home.

“Indeed inside families as is well known in my own case,” he said, adding those views needed to be treated with respect.

Opposition Leader Bill Shorten, who will introduce the private bill to parliament, says the time is right for marriage equality in Australia.

“I think Australia needs to move forward and catch up with the times,” he said.

Shorten said he would be shocked if the government didn’t debate the issue.

Deputy Labor leader Tanya Plibersek is refusing to say whether she will continue to pursue a campaign that aims to force her colleagues to support same-sex marriage legislation in parliament.

Plibersek batted away questions from reporters at Parliament House on Wednesday about her plan to have the ALP national conference force a mandatory vote on Labor MPs, preferring to talk about the private bill.

“I’m pushing for the private member’s bill … I’m pushing for a free vote in the Liberal Party,” she said.