Senator confirms 'hairs' oath, after challenging King

An Indigenous senator who verbally attacked King Charles has shrugged off criticism, saying she's received overwhelming support for her anti-monarchy protest.

Lidia Thorpe hurled a volley of abuse at the King during a reception in Parliament House in Canberra on Monday, telling the sovereign he was not king of Australia.

"You are not our king. You are not sovereign," she shouted.

"You committed genocide against our people. Give us our land back. Give us what you stole from us - our bones, our skulls, our babies, our people.

"You destroyed our land. Give us a treaty. We want treaty."

Asked on Thursday, about the public blowback from her actions, Senator Thorpe said it was "just another day in the colony".

"I wanted to send a message to the King, I got that message across. The whole world is talking about it," she told Nine's Today program.

"My people are happy because my people have been protesting for decades and decades, as you all know, for exactly this.

"So the message has been sent, delivered. Now it's up to the King of England to respond."

The senator for Victoria again rejected coalition calls for her to resign from the upper house.

She also confirmed that she swore an oath of allegiance to the late Queen's "hairs" rather than her heirs, when taking her seat in 2022.

"Swearing allegiance to someone else from another country, whose ancestors have done a lot of damage to my ancestors, I think is completely inappropriate," she said.

"I have a Senate seat for the next three and a half years, and I'll be using that to get justice for my people."

The federal opposition is examining the senator's eligibility to sit and take part in upper house proceedings under section 42 of the Constitution.

"The coalition will explore options and consider legal opinions as to the implications of Senator Thorpe's admission," the coalition's leader in the Senate Simon Birmingham said.

Constitutional lawyer Anne Twoomey told AAP on Thursday the words the senator spoke aloud were beside the point because she had also signed a written oath.

The opposition is also considering moving a censure motion against Senator Thorpe when the upper house sits again in November.

The federal government's leader in the Senate, Foreign Minister Penny Wong, said Senator Thorpe's admission about her oath was "an unusual thing".

"I have to say, we're all part of an institution that is the parliament and our democracy, and within that, we have very different views," she told ABC television.

However, Senator Wong said Senator Thorpe needed to "reflect on the institution of which she is a part, and how she wishes to play a role in that institution".

Senator Thorpe also defended taking a salary for sitting in the Senate, saying "it's paying the rent".

"I'm getting paid by the colony to bring up the issues that my people raise with me," she said.

Labor Senator Katy Gallagher also said Senator Thorpe needed to consider her position.

"We need to work out a way to ensure that the institution of the Senate ... is upheld and respected, and I think that's at times challenged with some behaviour in particular from Senator Thorpe," she told ABC radio.

"She also does like the attention that comes from these ... public displays.

"We'll work with people across the chamber about what the appropriate response is."