Frontbencher Scott Morrison remains convinced that a referendum is the best and fairest way to move forward on same-sex marriage.
Attorney-General George Brandis has dismissed the suggestion of changing the constitution, labelling Mr Morrison's proposal as "entirely unnecessary".
But Mr Morrison said a referendum ensures a binding outcome in which the views of all Australians are reflected.
"I believe the best way to address this issue definitively, so all Australians can have their say, is to have a referendum," he said in Adelaide on Friday.
"Every Australian of voting age gets to have their say, and is required to have their say.
"From whatever community they might come from, whatever religious community, whatever ethnic community they might come from."
The Social Services Minister also said a referendum was fairer to the less populous states.
"The people of South Australia shouldn't have this issue determined ... by the bulk of numbers in the eastern states, any more than Western Australians or Tasmanians should," he said.
"People of the country who have different views on this, who are of good faith - that should be reflected."
However, there is little support from others in the Abbott ministry for Mr Morrison's idea.
"A referendum would cost a great deal of money, in fact only to achieve no outcome because there is no legal basis for a referendum," Christopher Pyne told the Nine Network on Friday.
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