The move has inflamed tensions between the conservatives and moderates in the party and set the stage for a lengthy parliamentary debate over religious freedoms and anti-discrimination laws.
"The government does not, would not countenance making legal discrimination that is illegal", Turnbull told reporters.
The bill also enshrines protections for people who hold views that marriage is only between a man and a woman, that sex should only be between married men and women, and that gender is only binary.
"That would be profoundly disrespectful and a rebuke to the people of Australia. They didn't vote to license more discrimination and that is what the Paterson bill does".
"We do not want a dictatorship of the majority in this country".
"The objective of the Bill is clear: it creates equal access to marriage while protecting religious freedom in relation to marriage", he said. Cormann said thought the Smith bill was "a good starting position" but thought it would need improvement to "strengthen religious protections".
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"This moment can't be the moment we literally do the opposite of what the people are saying".
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.
"Australia's anti-discrimination laws were amended in 2013 to enact important protections for LGBTI people in recognition of the unacceptable levels of discrimination. As a non-religious person, I should have no fewer rights to live my life consistent with my beliefs than anyone else".
A cross-party group of senators - led by Liberal Dean Smith and supported by senior Labor figure Penny Wong, amongst others - will introduce a private bill to the upper house on Wednesday, just hours after the survey result is announced.
The proposed bill has been heavily criticised by supporters of gay marriage with Alex Greenwich, co-chair of Australian Marriage Equality, claiming it has the potential to "divide Australians".
Senator Smith said he was hopeful the Yes vote would prevail, but even if Australians voted No he would still introduce the Bill to the Senate this week.