A Tasmanian local council meeting has descended into turmoil after councillors walked out following "uncalled for and divisive" comments surrounding January 26.

Alderman Marti Zucco and Louise Elliot walked out of Hobart City Council's first meeting of the year on Tuesday after Lord Mayor Anna Reynolds voiced her long-time support for changing the date of the nation's public holiday.

Evidencing a motion passed eight years previous, Ms Reynolds said support was shared by the Council of the day in 2017.

"The council at the time did so in recognition of how inappropriate it is for what is meant to be a day of national pride and unity to be held on the day that the British Army started colonising the Australian east coast," Reynolds said, Pulse Tasmania reports.

After Mayor Reynolds earlier referred to Australia Day as Invasion Day, Alderman Zucco decided to leave.

"Lord Mayor when you're finished please let me know and I'll come back in," Mr Zucco said as he left the Council's chamber, promptly followed by Ms Elliot.

In the meeting, Mayor Reynolds went on to say January 26 is a "difficult and divisive day for the Aboriginal community and others in the community who are concerned about this period of Australian history," according to Pulse.

Following the meeting, Mr Zucco said he left during Mayor Reynolds' "rant" as he believed her commentary would "drag the council down the path of further division within our community".

"The Lord Mayor was totally out of line, irrespective of council policy and of personal opinion about changing the date," Mr Zucco said, according to Pulse.

"But to declare Australia Day as Invasion Day is uncalled for. One of my best mates for over 58 years is of Tasmanian Aboriginal descent.

"So don't play that racist card on me. We are all Australians."

On Sunday, Mayor Reynolds spoke at Hobart's January 26 rally at Parliament Lawns.

There she said she would remain committed to taking "positive and progressive steps locally" to fight for a date change.

"It's shocking to me that more Australians and indeed more leaders don't see how unfair and mean it is to celebrate our nation's spirit on the day that a violent colonisation of a First People began," Mayor Reynolds told the record crowd.

"No other colonial country in the world does something so jarring, so insensitive and so intentionally divisive.

"When we stand together and we work together, we can do important things locally that can lead the way nationally.

"We can make progress locally even while we might see backwards steps happening nationally and internationally."

At the rally, Mayor Reynolds was recognised by Tasmanian Aboriginal Centre campaign coordinator Nala Mansell as a "key" figure in the removal of the "dirty, terrible" statue of former Tasmanian premier William Crowther from Hobart's Franklin Square.