Australian Senator Dean Smith has introduced a historic marriage equality bill to the Australian parliament.

Senators from across the spectrum rose to endorse it just a day after the results of a national survey revealed more than 60% voted in favour of removing discrimination in the marriage law.

After the overwhelming mandate with 61.6% in favour of same-sex marriage, Smith and the cross-party grouping of Labour, the Greens, the Nick Xenophon Team and Derryn Hinch lost no time in introducing the bill and commencing debate on Thursday.

In his second reading speech, Smith thanked Australia on behalf of LGBTI people, saying the result had shown “a glimpse of the country we all yearn for, a country that is fair-minded, generous and accepting”.

Speaking from his perspective as a gay Australian, Smith said “the biggest hurdle” for LGBTI people is often “that of self-acceptance”. Inclusion in the institution of marriage is vital because “nothing speaks more of acceptance than marriage”, he said.

Smith credited Liberal MP Warren Entsch for his advocacy for same-sex marriage before any LGBTI Coalition members were elected to parliament, saying the bill was “more Warren’s than anyone’s, we simply walk in the track he has laid”.

As a fight in the parliament looms with conservatives set to push for greater protection for religious freedom and conscientious objection, Smith said the postal survey and the bill dealt only with changes to the Marriage Act, and debates about freedom of expression and living out one’s beliefs should be left for another day.

“Amendments that seek to address other issues or which seek to deny gay and lesbian Australians with the full rights, responsibilities and privileges that they already have will be strenuously opposed,” Smith warned.

“Australians did not vote for equality before the law so that equality before the law that is already gained be stripped away.”

Smith’s speech was applauded by Labour, the Greens, the Nick Xenophon Team and Coalition MPs Trent Zimmerman, Tim Wilson and Trevor Evans, and senators George Brandis, Simon Birmingham, Marise Payne, Linda Reynolds, Jane Hume, Bridget McKenzie, James Paterson and Jonathon Duniam.

Senior conservatives including the finance minister, Mathias Cormann, and the resources and northern Australia minister, Matt Canavan, were absent from the chamber.