Victoria is the only state or territory that requires parliamentarians to swear allegiance to a new monarch as part of its constitution.

That event has not occurred since February 14, 1952, eight days after the death of Queen Elizabeth II's father King George VI.

Small groups of members from both houses were called to take an oath or affirmation on Tuesday and the process took about half an hour.

Victorian Greens leader Samantha Ratnam labelled the convention outdated, although the party's four MPs fell into line while wearing T-shirts and accessories emblazoned with the Aboriginal rights phrase, "always was, always will be".

"We're here as Victorian MPs to swear allegiance to King Charles III, a new head of state decided for us, but not by us," Ms Ratnam told reporters before the ceremony.

"This is a really important time to reflect on the role of the British monarchy going forward in Australia, the impact of colonisation and the need to move forward in this country with a treaty and with a republic."

Ms Ratnam, born in England and raised in Sri Lanka before escaping civil war there, said she was one of millions who had "different experiences" of the monarchy.

The Victorian and Tasmanian Greens have joined the party's federal leaders in calling for more discussion about Australia becoming a republic after the Queen's death.

"Surely we've got the guts to have a national conversation ... what better time than this?" Tasmanian Greens leader Cassy O'Connor told state parliament on Tuesday.

Prime Minister Anthony Albanese insists it is too soon to discuss changing the country's system of government and has ruled out a republic referendum this term, prioritising an Indigenous voice to parliament.

A Roy Morgan poll, conducted via SMS on Monday after King Charles became Australia's head of state, indicates a second referendum on a republic would be doomed to the same fate as 1999 if held now.

Of the more than 1000 survey respondents, 60 per cent thought Australia should remain a monarchy while 40 per cent wanted it to become a republic with an elected president - a five percentage point fall since 2012.

Poll results aside, Victorian Premier Daniel Andrews agrees with the prime minister that now is not the time for talk of change.

"The debate may well be appropriate at another point," Mr Andrews said before leading a condolence motion that lasted more than three hours in the state's lower house.

Other condolence motions were held in the Tasmanian, NSW and WA parliaments on Tuesday before they adjourned as a mark of respect.

NSW Premier Dominic Perrottet expressed the state parliament's "profound sorrow at the death of our late beloved sovereign" and moved a second motion to congratulate the new monarch.

The motions passed without opposition but the NSW Greens did not support suspending parliament, arguing MPs must keep working amid cost-of-living and climate crises.

The final sittings of Victorian parliament before the November state election were scheduled for this week but have been pushed back until next week.

Australian Associated Press