Brisbane City Council opposition leader Peter Cumming, making his public position on the controversial date known for what he said was the first time, diverged from federal Labor leader Bill Shorten's opposition to moving the national day.

A handful of councils nationwide, including Darebin and Yarra in Melbourne and Fremantle in Western Australia, have scrapped Australia Day celebrations and shifted citizenship ceremonies to other dates, provoking the ire of the federal government.

Cr Cumming said he would be happy with a a national agreement to shift the date away from January 26, the anniversary of the First Fleet's arrival in Sydney Cove.

But he would not support calls from Greens councillor Jonathan Sri, acting amidst a heightened date change push from the party nationally, for the council to shift its celebrations and citizenship ceremonies.

"It would be good to have a day that Aboriginal people felt they could celebrate as well," the Wynnum Manly Ward councillor said.

"I probably don't see a lot of sense in the council doing it because at the end of the day it's a national holiday.

"I think it's the same all around the country so it would be a case of trying to get agreement from the federal government and... general community and Aboriginal community to come up with a suitable day.

"It's got to be handled on a nationwide basis."

All states and territories agreed to celebrate Australia Day on January 26 in 1988 and the date was officially established in 1994.

Even with support from Cr Cumming and his Labor colleagues, Cr Sri's push would have been doomed thanks to the LNP's dominance in the 26-member council.

Lord mayor Graham Quirk reaffirmed his opposition to moving the day on Tuesday, characterising the year's biggest citizenship ceremony as a "key part of Brisbane's vibrant and inclusive reputation".

He said all citizenship ceremonies recognised the traditional owners with a comprehensive Welcome to Country.

"My position as lord mayor is very clear: Council has no intention of changing the date of our Australia Day commemorations," he said.

The opposition from both key sides of local politics came after both Cr Sri and indigenous activist Sam Watson, one of the organisers of Brisbane's annual Invasion Day protest march, called for change.

Mr Watson said Australia Day needed to be moved, but January 26 should be kept as a reminder of the anniversary of the day the "foreign invasion of our sovereign land commenced back in 1788".

"You can't expect victims of a criminal act to then celebrate the anniversary of the commission of the criminal act," he said.

Mr Watson said the first fleet's landing was the day violence, genocide, loss of traditional lands and destruction of sacred sites began and celebrating it was an "insult".

Cr Sri had called for Labor to "get off the fence" and describe its position on the contentious issue, pledging to try to raise the issue at the first council meeting of the year.

"It's important to start by recognising that just because someone rocks up to a party or a celebration on invasion day, it doesn't automatically mean they're a racist," Cr Sri told ABC Radio Brisbane.

"I think most people that celebrate on the 26th of January say they're celebrating the positive aspects of modern Australia.

"But even if you're not actively celebrating the genocide and the massacres and the stolen land and the stolen children, it's still pretty mean and pretty cruel to be partying on the anniversary of the invasion on the date that causes so much pain to so many people."

CORRECTION: An earlier version of this story incorrectly quoted Cr Sri.