The Victorian senator said Greens MPs, members and supporters had voiced support for the Voice, which was "at odds" with grassroots activists calling for Treaty before Voice.

Senator Thorpe earlier announced she could no longer remain in the party as a result, adding her resignation left her now able to "speak freely" and "without being constrained".

The announcement follows a party retreat last week where the Voice and other key policy matters were discussed. Senator Thorpe did not attend the retreat.

Greens leader Adam Bandt said he was "truly sad" over Senator Thorpe's resignation, wishing she had stayed on in the party.

Mr Bandt also added the party would hold another meeting on Monday night to further consider its final position on the Voice.

The now-independent senator Thorpe, whose term ends in 2028, will join a handful of key crossbench senators the Albanese government will need to deal with to pass legislation through the upper house.

"Now, I will be able to speak freely, on all issues, from a sovereign perspective, without being constrained by portfolios and agreed party positions," Senator Thorpe said.

"... I want to represent that movement fully in this Parliament. It has become clear to me, that I can't do that from within the Greens."

The senator said she would not yet formally declare her position on the Voice but would continue to vote with the Greens on climate policy.

Senator Thorpe thanked Mr Bandt and deputy leader Mehreen Faruqi but would not comment further on her time with the Greens, taking no questions at the press conference.

Mr Bandt said the passionate senator left the Greens with "an enormous amount of respect".

"She is a fighter for her people. She has helped put Treaty, and raising the age of criminal responsibility on the parliamentary agenda," he said on Monday afternoon.

"I thank her for her commitment to continue to vote with the Greens on climate in the Senate."

Senator Thorpe last week welcomed a government assurance that the Voice proposal will not cede First Nations sovereignty, which she had repeatedly raised concerns about with colleagues and in public comments.

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An agreement with her party colleagues struck last week allowed Senator Thorpe to vote against the proposal while remaining the party's spokesperson for Indigenous matters.

Senator Thorpe said she wanted to become the leader of the "blak sovereignty" movement.

"My focus from now is to grow and amplify the Blak Sovereign Movement across the nation. I have spent my entire life fighting for justice, to defend our sovereignty, to save Blak lives. That is my goal," she said.

"My strength and conviction comes from a lifetime of activism, from my ancestors and from my matriarchs, who continue to say to me every day, 'keep infiltrating, keep your integrity, keep the fire burning, keep our fight alive'.

"To my mob, I say this - your strength is my strength, your fight is my fight, your struggle is my struggle. I'm ready for what comes next in the fight for a future where our kids are with their families, where our people are not killed in custody, where the chains that the system wraps around our people are lifted."

Prime Minister Anthony Albanese has called on politicians from all sides of the chamber to come together and support the proposed Voice to Parliament.

In a speech delivered on Sunday, Mr Albanese said politicians should reject the "false choice" critics have posed between constitutional recognition and practical outcomes for Aboriginal and Torres Strait Islander people.

It's expected legislation to hold the referendum will be introduced in the second half of 2023.