The Palmer United Party will back the repeal of the carbon tax only if legal guarantees are in place to ensure energy companies pass on savings to consumers.
He also wants the retention of key climate bodies, set up by Labor but due to be axed by the coalition, and the renewable energy target until at least 2016.
A spokeswoman for Mr Abbott said he welcomed the commitment to repeal the carbon tax and would take strong action to ensure electricity price cuts flow through.
Mr Abbott would "consider the detail" of further amendments, the spokeswoman said.
Mr Palmer said the prime minister was "very open" to his ideas.
"It was a constructive meeting, something you'd hope from a prime minister that had the responsibility for these serious issues in Australia," Mr Palmer said.
The mining magnate has also raised the idea of a new emissions trading scheme with a zero-dollar starting price that will only be activated when there is similar action from Australia's key international partners.
But he says he will still vote for the carbon tax repeal even if his ETS proposal is voted down.
Labor and the Greens have welcomed the PUP support for the renewable energy target and bodies such as the Climate Change Authority but are puzzled by his ETS policy - particularly given the carbon tax will transition to an ETS in a little more than 12 months.
But Mr Palmer insists Australians shouldn't have a working scheme until other countries introduce something similar.
"When this condition is met then the parliament of the day and the government will decide what the price for carbon should be by reference to our trading partners, so it doesn't disadvantage Australians," he said.
Labor says it will not back a repeal of the carbon tax without a redible emissions trading scheme in its place.
Opposition environment spokesman Mark Butler says Mr Palmer should back "Labor's fair dinkum ETS".
The repeal bills are now likely to pass in the Senate sitting fortnight starting on July 7 with the PUP senators, the Motoring Enthusiasts' Ricky Muir and two other crossbenchers voting with the government.
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