Queen Elizabeth II dies: Monarchist League chairman Eric Abetz demands Greens leader Adam Bandt apologise for 'insensitive' republic post

And Finance Minister Katy Gallagher has insisted the Queen's seven-decade service should be recognised for a period before "no doubt extensive debate over Australia's future".

Reacting to the monarch's passing on Twitter on Friday, Mr Bandt said "our thoughts are with her family and all who loved her".

But the Greens leader also urged Australia to "move forward" by signing a Treaty with First Nations Australians and becoming a republic.

Greens senator Mehreen Faruqi went further than her leader, reiterating his calls for a republic and saying she could not mourn the leader of a "racist empire built on stolen lives, land and wealth of colonised peoples".

Former Liberal senator Eric Abetz, picked to lead the Australian Monarchist League last week, blasted the timing of the comments.

"I hope that on self-reflection, he will have the decency to apologise and accept that what he said was completely unacceptable and as insensitive as any human being in public life in recent times," Mr Abetz told ACM.

Mr Abetz, who met Queen Elizabeth II on multiple occasions, described her as "gracious poised, warm" but said there was "no misunderstanding that she was the Queen".

"She combined the royalty aspect and the gravitas of the monarchy, along with a personal warmth, which was one of the most endearing features about her," he said.

Mr Abetz recalled accompanying the Queen at an event in Australia, where she spotted an attendee who was shyly "trying to hide himself away".

"She smiled with a sort of twinkle in her eye and deliberately went off the track to see him," he said.

"Afterwards, it was so obvious that it was such a delight for him that the Queen had gone out of her personal way to say hello to him."

The Queen's 70-year reign saw her become almost synonymous with the Royal Family itself, with the vast majority of Australians never having lived under another monarch.

But Mr Abetz assured Australians her successor King Charles III had spent decades learning from "an absolute exemplar as his mentor".

"We have been being especially blessed to have Queen Elizabeth II as the monarch," he said.

"But at the end of the day, it's the institution as opposed to the individual that may or may not be holding that position."

Despite being a key figure in the doomed 1999 republican push, former prime minister Malcolm Turnbull appeared emotional on Friday morning while discussing the Queen's death.

Mr Turnbull's successor Scott Morrison said Queen Elizabeth's personal dignity made her a "source of strength for many people", regardless of their standing a republic.

"She transcended that issue, she transcended it," he told the ABC.

"She was more than just the Queen of England ... she was a global figure like arguably no other, in her constancy and her endurance."

After signing a public condolence book at Parliament House, Senator Gallagher said there was "enormous fondness for the Queen across republicans and monarchists".

"I think it is appropriate that we remember her in that regard before there is no doubt extensive debate on Australia's future," she said.

"We haven't seen anybody like her. She's passed away in the last 24 hours, and I agree that we should respect her service."

Former prime minister John Howard, a staunch monarchist and leader during the 1999 referendum, said he did not want a "vigorous debate" on the republic so soon after the Queen passed.

"I have views. You know what those views are. But there'll be time [to discuss that] because we're a democracy," he told reporters.

"I've always said that the monarchy stays or goes according to the will of people."

Earlier, the Australian Republic Movement issued a statement paying "due respect to the significant contribution" made by Queen Elizabeth II.

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The ARM said the Queen had served "admirably" and "rose to become a respected representative of Britain and the Commonwealth".

"We are deeply saddened by the news of Queen Elizabeth's passing and express deep gratitude and thanks for her service to the Commonwealth," ARM chairman Peter FitzSimons said.

"During her reign, Australia has grown into a mature and independent nation. It is unlikely we will ever see a monarch as respected or admired by the Australian people again."