Although the result of the poll will not be binding on the government, Prime Minister Malcolm Turnbull has promised that a bill to change marriage laws will be forthcoming.
'While the Law Council does not endorse every detail of the Smith Bill it represents a better balance from a human rights perspective and represents greater fairness, including those affected by winding back anti-discrimination laws, ' Ms McLeod said.
"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", he said.
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.
Some 22 bills seeking same-sex marriage have been introduced into the federal parliament since 2004.
"The consensus position was the position that the Greens would support", he said, saying senators should "think very very carefully about entrenching discrimination to support your colleagues rather than this bill".More news: Greek life suspended after Texas State sophomore found dead in pledging incident
In contrast, Smith's bill allows exemptions only for religious organizations and ministers.
Senator Smith is aiming to introduce his bill to the upper house on Thursday.
The Equality Campaign has rejected the marriage equality bill put forward by Senator James Paterson as nothing more than a license to discriminate.
Well, the Senate could begin debating it as early as tomorrow.
The Australian Bureau of Statistics said Wednesday 62 percent of registered adults who responded voted for the reform in an unprecedented survey.
Paterson's bill allows refusal of wedding services from both religious and secular parties.More news: Cammalleri traded to Oilers by Kings for Jokinen
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".
"It's clearly a good bill to start with", he said.
After a high no vote in western Sydney, the Labor MPs Jason Clare, Linda Burney, Tony Burke, Michelle Rowland and Ed Husic confirmed they would vote in favour of marriage equality, despite majorities against it in their electorates.
Nevertheless, discussions are well under underway as to how same-sex marriage might be legislated.
Ms McLeod said the Marriage Amendment (Definition and Religious Freedoms) Bill 2017, endorsed by five government members including Senator Dean Smith, already extended existing protections for freedom of religious expression in the context of marriage and was a reasonable compromise.
One Nation, which controls three votes in the Senate, has reserved its position.More news: Airbus seals record 430-jet deal to outshine Boeing in Dubai
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