But the Liberal senator David Fawcett, who chaired the Senate committee inquiry into same-sex marriage from which Smith's bill was drafted, told Guardian Australia the inquiry had concluded that religious freedom needed to be positively protected.
Same-sex marriage is on track to be legalised before Christmas after draft laws were introduced to the Senate.
"The Prime Minister and I, and other members of the government, have always said that there should be strong protections for religious freedom and freedom of conscience". 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".
Senator Smith's bill has been co-sponsored by eight senators from across the political spectrum, and both Labor and The Greens have thrown their support behind the bill.
Liberal frontbencher Christopher Pyne has said the bill could be debated in parliament as early as this week.
"At last, same sex couples will be able to get married, as I have long advocated", Senator Paterson said.
Labor's caucus has already passed a motion supporting the Smith bill as an acceptable balance between marriage equality and religious freedom.
Victorian Senator James Paterson has proposed a rival bill that would "preserve" religious freedoms and allow businesses to decline to take part in same-sex weddings.
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Greens leader Richard Di Natale warned opponents against amendments which would have discriminatory impacts.
"It is clear the majority of senators believe my colleague Senator Dean Smith's Bill is where we should start", Senator Paterson wrote on his Facebook page.
The Australian Bureau of Statistics said Wednesday 62 percent of registered adults who responded voted for the reform in an unprecedented survey.
If the Senate passes the bill by November 30, the House of Representatives could begin debating the bill on December 4.
"There won't be a government position, there won't be a party position", Senator Cormann said.
Former prime minister Tony Abbott, whose Warringah electorate voted 75 per cent "yes", appeared to favour abstaining in the final vote when asked about his position on 2GB radio.
"If the Australian people do vote yes, they're not going to look kindly on the same group of people who have urged a 'no" vote not accepting the outcome and trying to delay further, ' she said. "I'm not going to frustrate the will of the public", Mr Abbott said.
The Paterson bill ensures exemptions for ministers of religion and celebrants with genuine belief and allows a limited form of conscientious objection, and also seeks to protect freedom of speech and guarantee the right of parents to opt their children out of school classes that conflicted with their values.