The minor party's change of heart paves the way for the Albanese government to pass the federal ICAC bill by mid-week.

Debate over the integrity watchdog began in the Senate on Monday with the opposition moving amendments that would require the commissioner's role be backed by three-quarters of its parliamentary oversight committee.

Greens justice spokesperson David Shoebridge initially said his party would agree to support the Coalition if it could not get the numbers to support its preferred change to appoint a non-government chair.

But on Tuesday morning, the Greens senator said the minor party had changed its mind after consulting with other crossbenchers.

Instead, the Greens will team up with ACT senator David Pocock to push for appointments to be approved by a simple majority in the committee - half of the committee plus one.

The committee of 12 is chaired by a government member with five government committee members but features two crossbenchers and four opposition seats.

"It removes the absolute power from the government of the day for this critical appointment," he said on Tuesday.

"But it also removes a veto from the opposition. No opposition of themselves can simply veto an appointment."

Senators will continue debating the bill and proposed amendments throughout Tuesday and could reach a vote as early as the afternoon.

Senator Shoebridge said Attorney-General Mark Dreyfus was "not minded" to support the Greens-Pocock amendments but hoped the federal government would change its mind throughout the day.

The Greens remained committed to passing the anti-corruption bill this sitting period and were unlikely to vote against the Labor government, even if it rebuffed the crossbenchers' amendments, he said.

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Senator Pocock added the government needed to bring crossbench members into the tent regarding the appointment process.

"When it comes to appointing the commissioner and inspector, there was a strong argument that it shouldn't just be up to the government of the day," he said on Tuesday.

"They should at least have to convince a crossbench or two or potentially the opposition that this is the right person for the job."

Mr Dreyfus earlier slammed the opposition's proposal, put forward by Liberal senator Michaelia Cash, saying it would provide "an effective veto" on creating the body.

"The government will not be supporting that amendment and, indeed, I would call on the Liberal Party to withdraw that amendment," Mr Dreyfus said on Monday.

Coalition legal affairs spokesperson Julian Leeser said the opposition didn't want to create road blocks to establishing an anti-corruption commission, saying instead the amendments would stop future appointments from becoming a "political issue".

"That is an outrageous slur and we call on the government to withdraw that assertion," he said.

"The amendments that we are moving in the Senate are the same ones we moved in the house. The amendments ensure that the commissioner and inspector are genuinely independent, and they support public confidence in the commission."