Parliament will ultimately decide what form the bill will take.
Labor Senator Penny Wong said she hoped the Prime Minister would stand up against the suggested laws.
Mr Brandis said parliament would start the debate on same-sex marriage legalisation with Senator Smith's bill, if a "yes" vote is victorious.
"If the parliament opts for a narrower bill with fewer protections, I fear we will see some Australians seek to impose their values on others, with court cases and other legal mechanisms", he said in a statement announcing the draft bill.
Brandis flagged plans to amend the bill when it goes to committee to extend the right of conscientious objection to from ministers of religion to include civil marriage celebrants. He also called for a provision to state that "nothing in the bill makes it unlawful for people to hold and to express the views of their own religion on marriage".
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"I will now work constructively with my parliamentary colleagues over the coming weeks on amendments to ensure that the strongest possible protections for the freedoms of all Australians are enshrined in the final legislation".
Cabinet minister Mathias Cormann said his personal instinct was the Smith bill was "probably a good starting position" because it had been subject to a cross-party Senate committee process.
Significant ground was given on all sides and the Greens made significant concessions Di Natale said, to create the cross-party Smith bill.
"It's already against the law", Senator Brandis said.
Earlier, at a rally in Melbourne, Shorten promised: "Today we celebrate, tomorrow we legislate".
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During a news conference in Manila, the PM repeatedly fielded questions on whether he would stand up to conservatives who are pushing for changes to the law, which allow people to refuse services to same-sex couples.
In a further rebuke, he said while parliamentarians would be entitled to put forward and debate amendments, he believed ideas such as Senator Paterson's "would have virtually no prospect of getting through the Parliament".
Senator Matt Canavan told ABC News24 that he would respect the wishes of Queensland and would not oppose a same-sex marriage bill, but added he "won't support a bill that diminishes fundamental human rights", arguing that the Smith bill was not "adequate". This Bill will encroach on many of these protections in an extraordinary and perilous way'.
Various opinion polls point to a majority "yes" vote, possibly as high as 60 per cent.
Western Australian Senator Dean Smith is expected to introduce his Marriage Amendment (Definition and Religious Freedoms) Bill 2017 to Parliament later Wednesday.
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One Nation, which controls three votes in the Senate, has reserved its position.