Tensions within the government over same-sex marriage have erupted again with conservative MPs warning Prime Minister Malcolm Turnbull that allowing a free vote on this issue would be a "betrayal" of the Coalition's election commitments.

Fairfax Media reported on Saturday that moderate MPs are preparing a push for the Coalition to abandon its policy that a national plebiscite should be held before any vote in the Parliament.

Tasmanian Senator Eric Abetz says the Turnbull government should stick with its plebiscite policy

Same-sex marriage supporters in the Liberal Party argue for a vote to be held before the May budget and could raise the issue in the party room within the next fortnight.

Former cabinet minister Eric Abetz said: "The Prime Minister has made it crystal clear that the government's position is for a plebiscite or nothing.