Under the reworked scheme unveiled by the prime minister on Thursday, anyone earning less than $150,000 will receive a larger tax cut while those earning more are in line for a smaller benefit than earlier promised.
The changes to the original stage three tax cuts that were first implemented by the coalition will need to pass parliament before they are due to come into effect in July, with the government needing the support of the Greens and crossbench.
But Greens leader Adam Bandt urged for the government to go further in its tax plan to provide greater cost of living relief.
"We now have the chance ... to really tackle inequality and the cost of living and housing crisis in this country," he told ABC Radio ion Friday.
"If we're going to change the legislation, then we should do it in a way that really supports low and middle-income earners."
But Finance Minister Katy Gallagher said she was confident of the cuts gaining the support of the upper house.
"The easiest way through the Senate is for the opposition to back these in and back in bigger tax cuts to millions more Australians," she told ABC TV.
"If they decide to oppose that, we will leave them to explain that, then we will work with other senators to get it through. This is the proposal we will be taking. There is no other proposals."
Opposition Leader Peter Dutton likened the changes to the tax cuts as a "betrayal", challenging Anthony Albanese to an early election on the issue.
"It's just a major break of trust ... the prime minister promised this on over 100 occasions, it's not just some throwaway comment that he made at a press conference," he told Nine's Today program.
"It's not just 1.8 million people who are worse off under this package, but over the coming years it's going to be for over four million Australians who are affected by it because of bracket creep."
However, the coalition is yet to announce whether they would repeal the stage three changes, should they win the next election.
Shadow treasurer Angus Taylor said the opposition remained in favour of the original stage three plan.
Reserve Bank Governor Michele Bullock is comfortable the reworked scheme won't fan inflation. (Bianca De Marchi/AAP PHOTOS)
"There were benefits to lower income earners in the earliest stages, of course, and the third stage is all about taking out that bit, that 37 cents threshold and in the process, dealing a real blow to bracket creep," he told Sky News.
Government Services Minister Bill Shorten said the measures were in response to growing cost of living pressures, particularly those faced by average-income earners.
"When your information changes, your conclusions change, the reality is that there's a cost of living crisis for Australians," he said.
Treasury advice asserts the tweaks are "broadly revenue neutral" and would not fuel inflation, which is moderating in response to a series of interest rate hikes but remains above the target range.
The key economic agency also expects the reworked scheme to boost labour supply more than the original version, particularly for women, taking pressure off consumer price growth over time.
Reserve Bank Governor Michele Bullock is also comfortable the reworked scheme won't fan the flames of inflation, based on the federal treasurer's remarks.
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