But the government has said it cannot be done as protocol prevented it.

Meanwhile, ACT Indigenous Affairs Minister Rachel Stephen-Smith has said the territory government has taken a more "low-key" approach in celebrating Australia Day, saying the government did not apply for specific grants to hold events on the day.

This has come after a recent survey indicated most Canberrans don't actively celebrate the day.

Greens leader Shane Rattenbury wrote to Chief Minister Andrew Barr and Legislative Assembly Speaker Joy Burch in late 2021 with the proposal to fly the flags at half-mast on Australia Day 2022.

"I am writing to make what I hope you will consider a positive proposal for the territory's acknowledgement of Australia Day, one that recognises that for many Aboriginal and Torres Strait Islander First Nations people it is a day of mourning, not celebration," Mr Rattenbury wrote.

"I would like to propose that we fly the Legislative Assembly's and the ACT government's First Nations flags at half-mast on 26 January 2022 and begin an annual tradition that supports a conversation about our country's history and moves towards greater understanding."

Mr Barr responded to say this was not possible because it would contravene the flag protocol that all flags within a set needed to be flown at half-mast at any given time.

In an interview with The Canberra Times about how the ACT government marks the day, Ms Stephen-Smith said she felt it was not productive to debate something constrained by protocol.

"There are protocols that we just don't have any choice over and so having those arguments about whether we should or shouldn't do something we cannot do isn't particularly productive," she said.

"Where it's more productive is to talk about how we ensure that we are respectful and supporting our First Nations communities in marking the day in whichever way they choose to do that.

"Recognising that people will have invasion day or survival day events, alongside the people who are celebrating being part of Australia as it is today."

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Ms Stephen-Smith, who believes the date of Australia Day should change, said Canberra had an important role to play in events held by the Commonwealth but the ACT government made the choice to not host as many events.

"We have a role as the nation's capital but from our own perspective, we'll mark the event in a much more low-key way and put more of our effort into Canberra Day and Reconciliation Day," she said.

"Previously we've applied for Australia Day grants to hold much bigger events both on our own and in partnership with the National Capital Authority and the Australia Day council. We haven't really done that this year.

"That really reflects the feedback from the Canberra community that people haven't been participating in those events in the numbers that they used to."

Ms Stephen-Smith pointed to a recent territory government survey, through the YourSay panel, of more than 1700 Canberrans which showed most respondents had either neutral feelings towards or did not celebrate the day.

The survey, taken in July 2022, asked whether Australia Day made them proud to be from Canberra and 34 per cent agreed, 38 per cent were neutral and 28 per cent disagreed.

But only 17 per cent of people aged between 16 to 24 said Australia Day made them proud to be from Canberra and only 24 per cent of 25 to 34 year olds said they were proud of this.

"It's clear anecdotally and it's clear in the survey results that younger people are increasingly less comfortable in celebrating on the 26th of January," Ms Stephen-Smith said.

"They're recognising the hurt that it causes to Aboriginal and Torres Strait Islander community members and are not wanting to be part of that ongoing trauma for Aboriginal and Torres Strait Islander people of seeing people celebrate the invasion of the country."

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