Leader Adam Bandt says he wants no new coal and gas projects in exchange for the minor party's support to pass the laws in the Senate, arguing any gains made by the cap would be wiped out by new fossil fuel projects.
But Mr Bandt says the proposition is an offer, not an ultimatum.
"It's an offer that says, we will put aside our very real concerns with the Ponzi scheme elements of this plan where everything gets offset," he told the ABC's Insiders program on Sunday.
"We will put aside the fact that we think you've got a low target that will mean the end of the Great Barrier Reef and that you're re-heating Tony Abbott's safeguard mechanism.
"We will vote for it in full if you do one thing: Stop making the problem worse. Stop opening new coal and gas projects."
Mr Bandt floated legislating a climate trigger, where the environmental impact will have to be taken into account when assessing new projects.
"That's a solution. That's a suggestion that's worth having a look at," he said.
He also denied the Greens were being obstructionist, saying he understood Australia was going through an energy transition towards renewables and his argument only stood against new coal and gas projects.
"We're not talking about existing projects. There's enough in the system at the moment for us to go through the transition," he said.
"It just says don't make the problem worse."
Mr Bandt said while royalties for new fossil fuel projects could be in the order of hundreds of millions of dollars for the government's coffers, not acting to prevent climate-related disasters would be much worse.
"Look at the damage caused by the floods, fires and droughts if the climate crisis gets worse and how much is being spent by communities at the moment just dealing with all of that," he said.
"It's the only way to save our economy. It's a net benefit to the economy."
The Greens also want to block the government's signature $15 billion manufacturing fund from propping up fossil fuel projects.
Industry Minister Ed Husic said the government is involved in constructive discussions with both the Greens and cross bench about the reconstruction fund legislation.
"The Albanese government's $15 billion national reconstruction fund is one of the largest investments in manufacturing capability in living memory," he told Sky News.
"It's going to ensure we reduce our dependence on broken or concentrated supply chains and take the fight to inflation.
"The safeguards are also a big part of us being able to reduce emissions and increase jobs in the process as well."
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