A Liberal senator has given a strong indication he will support a bill for a free parliamentary vote on same-sex marriage.

Key points: Senator Smith says a senate committee consensus gave hope that a free vote could also find consensus

Senator Smith says a senate committee consensus gave hope that a free vote could also find consensus Finance Minister Mathias Cormann says Government's position remains unchanged

Finance Minister Mathias Cormann says Government's position remains unchanged Shadow attorney-general says Senate committee report is "heartening" and "removes stumbling block"

West Australian Dean Smith, who has previously floated the prospect of crossing the floor on same-sex marriage, has added his voice to a number of Government MPs renewing a push for a free vote.

"That is an active proposition and I would point to the Howard government," he told Sky News.

"This is not a revolution inside the Coalition — under the Howard government these issues were managed sensibly, people had an opportunity to put their concerns on the table, remedies were found."

A Senate committee has reached consensus on how the marriage act would be changed if legislation was passed, but senior ministers insist it does not change the Government's position.

Senator Smith said the committee, chaired by Liberal Senator David Fawcett, showed politicians could reach consensus on how to legalise same-sex marriage if a free vote was held.

The report called for religious celebrants to be allowed to refuse services to couples based on their religious beliefs, while civil celebrants would be required to marry all couples.

"The committee report will be a source of information — evidence if you like — that whatever bill is put forward does address some of those issues that were identified in that consensus report," he said.

Mr Smith said the Liberal Party's position on same-sex marriage was clear; that a vote was only possible through the plebiscite that was blocked by the Senate in October.

"I have never supported the plebiscite," he said.

"I would say to my colleagues that 56 per cent of Coalition voters have identified in a Newspoll, after the detail of the plebiscite was revealed, did not support the plebiscite."

Time for a free vote: Labor

Senior Coalition minister Mathias Cormann said the parliamentary report did not change the Government's position on same-sex marriage.

"The work that the Senate select committee did is in the scenario where a plebiscite were to make certain decisions, would have to have certain outcomes," he said.

Shadow attorney-general Mark Dreyfus said a committee report should give fresh momentum to the push for a free vote in Parliament.

"What's heartening about this report by representatives of almost all parties in this Parliament is that it shows consensus can be reached on the form of legislation," he said.

"It clears the way, it removes a very significant stumbling block."

Labor's Tanya Plibersek said the committee should be praised for reaching consensus despite "vastly difference perspectives".

"I think it is a real tribute to the work of those senators and the work of the Senate, that these complex issues have been able to be dealt with in a mature way," she said.

"It's now time for the next step, which is a free vote in our Parliament."