The Senate will aim to pass marriage equality laws this week after voters gave a resounding 'yes' result to the Turnbull government's postal survey.
Debate will resume on Monday in the upper house on a private senator's bill introduced by Liberal Dean Smith to change the marriage laws.
Labor senator Anthony Chisholm hopes it will be signed off this week.
"The Australian people gave a really strong endorsement of marriage equality," he told Sky News on Sunday.
"The way people are viewing politics at the moment it would be very dangerous if the Senate did delay."
Prime Minister Malcolm Turnbull scrapped the House of Representatives sitting that was also due to start on Monday to allow the upper house to deal with the same-sex marriage issue.
The lower house will take up the legislation next week.
The key concerns surrounding the new laws will be religious freedoms and parental protections.
Liberal assistant minister Angus Taylor says there will be room for people to put amendments
"We need to keep faith with all Australians in the way we put legislation in place," he told Sky News.
Not only for those people who said 'yes' to passing same-sex marriage legislation, but also those who said 'no' and those who said 'yes' who are concerned about these issues, he said.
Mr Taylor says he will be supporting these sort of protections.
"A majority of Australians believe these sort of things are important too," he said.
