Indigenous senator Lidia Thorpe said First Nations people were too often engaged in long, expensive and unfair legal battles.

"Too many sacred sites have already been destroyed," she said on Wednesday.

"We need better resources so traditional owners can fight back and assert their rights to country."

The Greens will push for the fund if the minor party ends up holding the balance of power in parliament after the next federal election.

The funds would be drawn from a billionaires and corporate super-profits tax proposed by the Greens.

Greens spokesperson for mining and resources Dorinda Cox said state-based legislation offered no avenues for appeal or the right to veto mining decisions.

"First Nations people do not have bags of cash lying around to take mining companies and corporate landowners to the Supreme Court to protect their cultural heritage," the Indigenous senator said.

"The Senate inquiry into the destruction of 46,000 year old caves at the Juukan Gorge show that legislation protecting country is weak.

"It was written in the interests of mining and development."

Senator Thorpe was kicked out of the Senate on Monday after yelling "black lives don't matter in the Beetaloo" following a failed attempt to stop $50 million in grants going towards exploration in the NT gas basin.

She said the major parties were beholden to donations from fossil fuel companies.

Australian Associated Press