Mr Turnbull was responding to Liberal senator James Paterson's bill, which would extend religious protections to allow private businesses to refuse goods and services for gay weddings if they have "conscientious objections".
Attorney General George Brandis, a marriage equality advocate, rejected exempting gay marriage from anti-discrimination laws.
Liberal senator Dean Smith wants a private member's bill on same-sex marriage.
"The Dean Smith Bill covers who could marry, and could refuse to marry".
"If it's legally and morally wrong to discriminate against one gay person, I don't know how it becomes right to discriminate against two".
Senator Smith said he respected the right of "every parliamentarian" to bring legislation and amendments to Parliament, but believed his Bill was the best way forward.
Senator Paterson said his bill would also include provision for people who were not religious to object to being involved in a same-sex marriage, if it went against their beliefs.
The survey results will be announced on Wednesday, but debate is intensifying on whether Australians who would refuse to provide gay weddings with a celebrant, venue, flowers or a cake should have added protection against anti-discrimination laws.
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When Indhuja opened the door, the jilted lover threw petrol on her, dousing her mother and sister in the process, report added. The report also said that when her parents put out advertisements on matrimonial sites for Induja, Akash threatened them.
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The suggested laws have been received by supporters of the "yes" vote as a "kick in the teeth" to the gay community and which would roll back the clock on anti-discrimination legislation.
In response to concerns over the controversial Safe Schools program, the bill would also allow parents to pull their children out of classes where they "genuinely believe" their kids are being taught a view of marriage inconsistent with their own.
The national director of Liberals and Nationals for Yes, Andrew Bragg, has said a marriage bill should be guided by three principles: "Firstly, existing discrimination in the Marriage Act should be eliminated; secondly, a strong protection for religious freedom should be provided; and thirdly, we should not reintroduce commercial discrimination in Australia".
"There will be a debate about how wide the exemptions would be, some would have them narrowly cast and some more broadly cast".
Senator Smith last night exclusively told The Sunday Times his Marriage Amendment (Definitions and Religious Freedoms) Bill 2017 would be tabled in Parliament the next day.
The ABS will announce the results of the survey at 10am AEDT tomorrow. If successful, the Prime Minister has said that parliament should resolve the issue before they break for Christmas.
Opposition Leader Bill Shorten said Labor would give the Smith bill "very favourable consideration".
It comes just days before the results of a nationwide postal survey are released to the public.