A split is widening within the Turnbull Government about whether religious amendments to same-sex marriage legislation should be debated this year or in 2018.

Key points: Conservatives in Coalition want to allow civil celebrants to reject weddings, protect religious charities

Conservatives in Coalition want to allow civil celebrants to reject weddings, protect religious charities Liberal senator Dean Smith's bill before parliament is widely supported, protects religious ministers from performing SSM services

Liberal senator Dean Smith's bill before parliament is widely supported, protects religious ministers from performing SSM services Liberal MP Tim Wilson says it's odd traditional opponents of a bill of rights are suddenly pushing for one

Conservatives want a variety of changes, including allowing civil celebrants to reject weddings, and protections for religious charities.

Senior conservatives Peter Dutton and Mathias Cormann want these issues dealt with next year, to help ensure same-sex marriage is legalised before Christmas.

But Treasurer Scott Morrison and Resources Minister Matt Canavan have today demanded religious protections be incorporated into the bill currently before Parliament.

"I think now is the time to deal with these matters in one job lot," Senator Canavan told Sky News.

"[During] the next two weeks of sitting in both chambers, my understanding is there's not a lot of other business.

"The practical reality is parliamentary years become busy, and it's hard to carve out the kind of time you need to discuss these weighty issues."

Parliament has begun debating Liberal senator Dean Smith's bill, which is widely supported and protects religious ministers from performing same-sex marriages.

But Senator Canavan has said part of an international human rights treaty should also be included in the bill.

The International Covenant on Civil and Political Rights (ICCPR) states "everyone shall have the right to freedom of thought, conscience and religion".

Mr Morrison agreed the bill needed to address "very fundamental issues of faith and belief".

"There are over 4 million people who voted No in this survey who are now coming to terms with the fact that, on this issue, they are a minority," he told News Corp Australia.

"We now need a bill that acts for 100 per cent of Australians, not 61 per cent.

"Whether someone is a member of an organisation that has a traditional view on marriage should be irrelevant to whether they can sit on a board, work as a doctor, work in the public sector."

Odd that conservatives now pushing for bill of rights: Wilson

Prime Minister Malcolm Turnbull last week said the Smith bill did not "impose any restrictions on religious practice or religious speech".

Same-sex marriage advocate, Liberal MP Tim Wilson, warned some of the changes being floated "may not be constitutional", including amendments relating to schools.

Some within the Coalition want religious protections to go further, for example by allowing parents to withdraw their children from school lessons that mention same-sex marriage.

Mr Wilson told Insiders that while the Federal Parliament had control over marriage, the schools system was run by the states and territories.

"I think they're going to find that might be a strong intervention into the power of the states to decide how to run state schools," he cautioned.

Mr Wilson said Parliament should be "very careful" about separately debating religious protections next year, saying this would push Australia towards having a bill of rights.

"It's an oddity to see many people who identify as conservative or socially conservative, who have traditionally opposed a bill of rights or charter of rights, now prosecuting this cause."

Labor frontbencher Andrew Leigh said he was also surprised by the group pushing for religious protections.

"I do find it odd that some of the same people who were saying that we need to weaken protections against racial hate speech are now saying that we need to change laws in the opposite direction on religious discrimination," he said.

"We can consider that issue, it's a pretty complicated one, but it can be kept separate from same sex marriage."