Senator Lidia Thorpe has quit the federal Greens after failing to find common ground with her party on a Voice to Parliament.

"This country has a strong grassroots black sovereign movement, full of staunch and committed warriors, and I want to represent that movement fully," Senator Thorpe said.

"It has become clear to me that I can't do that within the Greens.

"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 has been a vocal opponent of the proposed Voice, and was one of the Indigenous representatives to walk out of talks that led to the Uluru Statement from the Heart.

But while the federal Greens are yet to formally commit to supporting the Voice in a referendum, disagreement between Senator Thorpe and the party on how to respond has been publicly acknowledged.

Bandt 'tried' to keep Thorpe in Greens

Greens Leader Adam Bandt said he offered Senator Thorpe the possibility of being allowed to speak out separately on issues of the Voice, and he "wished" she had not resigned.

"I'm truly sad to see her leave the Greens," he said.

"Senator Thorpe leaves the Greens with an enormous amount of respect. She is a fighter for her people.

"I said to Lidia I felt she could continue to advocate for black sovereignty within the Greens. She has obviously come to a different view.

Senator Thorpe announced her resignation on the first day of the parliamentary year, as the Greens prepare to declare their position on the Voice.

Mr Bandt said he would not pre-empt the outcome of further meetings on the issue, including a party room meeting this evening.

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While Senator Thorpe did not take questions from reporters, the senator flagged she would still vote with the Greens on climate change.

The senator also said she was open to negotiating on the Voice in return for her support.

Last year, Senator Thorpe was stripped of her position as deputy leader in the Senate by Greens leader Adam Bandt after the ABC revealed she had been in an undisclosed relationship with an ex-bikie boss while serving on a parliamentary committee that dealt with organised crime.

Senator Thorpe's term ends in 2028, and she will sit as an independent on the crossbench.

With a minority in the Senate, the government will now need the support of the Greens plus two other crossbenchers on votes opposed by the Coalition.