Liberal frontbencher Alex Hawke is open to changing Australia Day's date if a majority support the shift, after Prime Minister Scott Morrison moved to cement January 26.
Special minister of state Mr Hawke said he would advocate against changing the date if it was put to a public test.
"Of course if the overwhelming majority of the Australian public take a view that it should be a different day that's what will happen," Mr Hawke told ABC Radio National on Monday.
"But this government supports it staying on January 26 and we think it's in step with the majority of public opinion."
Debate has again flared on the most appropriate date, with many indigenous people viewing January 26 as Invasion Day or Survival Day.
Mr Morrison has moved to cement the date by compelling local councils to hold citizenship ceremonies on January 26, to ensure Australia Day did not "fade away".
"It's one thing to say you are not going to change the day, but it's another thing to really actually believe it and continue to make sure it is our premier national day," he told the Nine Network.
"We are the proudest and the most successful migrant country in the world and that is the day of all days that we should be handing out citizenship to celebrate that day and to celebrate the great migrant country we are."
Opposition Leader Bill Shorten said he was happy to keep Australia Day on January 26.
Mr Shorten accused right-wing politicians of working themselves into a predictable lather over the annual public holiday.
"I'm not going to go down every rabbit hole of every thought bubble of every right-wing Liberal politician about Australia Day," he told reporters in the Northern Territory.
"I did say yesterday, so long as it's a public holiday, and if Australia Day falls on the weekend, so long as its on the nearest Monday, that's pretty much where I think we need to go."
Mr Shorten accused conservatives of stoking the flames over Australia Day instead of talking about apprenticeships, property tax breaks, aged care packages, power bills and stagnant wages.
Greens leader Richard Di Natale said popular opinion on the date was changing.
"Have a look at every capital city in a couple of weeks time when hundreds of thousands of Australians will march for justice for our First Nations peoples," Senator Di Natale told reporters.
He also called on Labor to vote against the government's citizenship ceremony changes in the Senate.
