Labor deputy leader Tanya Plibersek says she still wants the party to adopt a binding vote on same-sex marriage.
Ms Plibersek has seconded a private member's bill introduced by Labor leader Bill Shorten to change the Marriage Act.
However, Mr Shorten has stopped short of making it a firm party policy, arguing that some Labor MPs opposed to same-sex marriage should be allowed to vote with their consciences.
Ms Plibersek said while there had been significant progress on the issue within the party she still believed members should be bound to support the policy.
"I think marriage equality is a matter of legal discrimination, not an issue for a conscience vote," she told Sky News on Monday.
"But I have to say we are a lot further down the track to marriage equality then we expected."
Ms Plibersek said she expected the binding vote issue would be raised at the ALP national conference in July.
