As the split between Coalition MPs about how to legislate same-sex marriage continued to widen on Sunday, Greens leader Richard Di Natale wrote to Mr Turnbull to call for increased funding for organisations that have been struggling with increased demand.

"It's time that the government acknowledges the harmful effects of the 'no' campaign on the LGBTIQ community," Senator Di Natale said.

"I urge you to immediately redirect these funds in support services for the LGBTIQ community, particularly for young people, to respond to the issues being experienced as a direct result of the government's decision to undertake the postal survey."

Some mental health groups were forced to redirect resources to cope with a sharp spike in need from the gay community throughout the three-month campaign. 

ReachOut Australia, which spearheaded a pro-same-sex marriage campaign by five of Australia's top mental health services, saw a 40 per cent surge in young gay people seeking help. The group has called on the government to announce a "clean up" plan.

Federal Parliament is expected to legalise same-sex marriage in the coming weeks after 61.6 per cent of people voted "yes" in the postal survey.

But a fight over the legislation is intensifying as conservative Coalition MPs push for a variety of changes, including stronger religious protections.

The scope of those changes – and whether they ought be debated this year or postponed until 2018 – has become a major battleground.

While Liberal senator Dean Smith's widely supported bill allows religious ministers to refuse to perform same-sex marriages, conservatives want those protections extended to civil celebrants. They're also pushing for increased protections for religious charities.

While many Coalition MPs believe same-sex marriage should be legislated this year and further religious protections considered next year, senior conservatives including Treasurer Scott Morrison and Resources Minister Matt Canavan say they must be implemented in tandem.

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

He wants elements of an international human rights treaty – the International Covenant on Civil and Political Rights, which seeks to ensure freedom of thought, conscience and religion – incorporated into the bill. He also wants clauses to ensure that parents are able to pull their children from classes and courses that don't accord with their religious or moral views.

But Liberal MP Tim Wilson, an ardent supporter of same-sex marriage, said such ideas may not be constitutional.

"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 told the ABC.

Mr Wilson also said Parliament should be "very careful" with its approach to religious protections, saying it could be a step towards 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," he said.

Labor MP Andrew Leigh said: "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."

Mr Morrison said the bill needed to address "fundamental issues of faith and belief" and act for 100 per cent of Australians, not 61 per cent.