The bill is designed to give big polluters an incentive to cut their emissions by 4.9 per cent a year by 2030.

It has now passed the House and will head to the Senate, where the government now needs the support of two Senate crossbenchers. It could be ACT senator David Pocock or the Jacqui Lambie Network senators, and consultations are ongoing.

Former Greens senator Lidia Thorpe has not stated her position, but she said in February when she left the party that she would continue to vote with the Greens on climate.

The safeguard mechanism scheme will now have a hard, total emissions cap and a so-called "safeguard trigger" for ministerial intervention.

Prime Minister Anthony Albanese thanked the crossbenchers who had "engaged constructively" on negotiations.

"It says a lot about the state of the Liberal and National parties in 2023 that in spite of the election result they have excluded themselves from any participation," he said.

"They're the observers of Australian politics rather than the participants."

The Greens had previously demanded, as a condition of supporting the bill, the government commit to a possible world-first ban on new coal and gas projects. Despite the government needing the Greens' support in the Senate, the Climate Change Minister Chris Bowen has repeatedly rejected that key request.

There has been a compromise on both sides. The deal will still allow new coal, oil and gas projects to proceed but it is expected there will be fewer of them.

Mr Bowen said, "The alternative would have been to walk away from 43 per cent as a country and limit our ambitions to 35 per cent which was never an acceptable outcome for the Albanese government."

While not getting the coal and gas ban, Mr Bandt said there will be a pollution limit in law.

"There will be in law for the first time in this country a limit on the amount of pollution that these corporations including the coal and gas corporations, can pollute," he said.

"And if pollution starts to rise above that, and the minister doesn't take steps to fix it, they'll be breaking the law."

He said the government had agreed to accept other amendments, including that it will accept a safeguard trigger in the legislation. He said new projects that are proposed to enter the system will have to pass a pollution test and if new polluting projects look likely to breach a pollution cap, "then the minister has to do something about it".

"We have also put significant hurdles in the way of a number of the projects currently underway in the pipeline that the government and others have been backing," Mr Bandt revealed.

"The Beetaloo gas field will be required from day one to offset all of its emissions."

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Despite coming to deal, the Greens leader has taken a whack at the government.

"Negotiating with Labor is like negotiating with the political wing of the coal and gas corporations," he told reporters in Canberra.

"Labor seems more afraid of the coal and gas corporations than climate collapse. Labor seems more afraid of Woodside than global warming."

The legislation modernises the use of carbon offsets, Safeguard Mechanism Credits, to rein in greenhouse gas polluting projects and help Australia meet its international emissions targets.

The Coalition opposes the Labor revamp of the scheme introduced under prime minister Tony Abbott, but it is needed to meet 2030 and 2050 net zero targets.

Mr Bowen describes the safeguard mechanism retooling as an "ambitious" scheme to help achieve a 4.9 per cent reduction in emissions every year.

However, modelling commissioned by the Climate Council and the Australian Conservation Foundation has shown declines of 8.9 per cent may be needed by the end of the decade to keep within the emissions budget.

Meantime, the fate of the Albanese government's signature housing bill, the Housing Australia Future Fund Bill, remains uncertain with Labor yet to secure Senator Pocock's support.

The key crossbencher wants to see more ambition to address Australia's housing crisis, particularly for the ACT which is facing a 3100 shortfall for new social and affordable homes but is on track to get 500 under the proposed fund.

"We are in the middle of a housing crisis and we need government to do more," Senator Pocock said in a statement.

"I want to see this bill pass next week but I want to see it pass with a commitment to spend more year on year in social and affordable housing because that's what our communities need."