A new analysis says high-income earners are the overwhelming beneficiaries of the income tax cuts promised by the Morrison government after 2024-25, with more than 50% of the benefit going to the top 20% of taxpayers.

As Labor continues to mull whether or not to support stages two and three of the Coalition’s tax plan, the new work from the progressive thinktank the Australia Institute to be released on Friday underscores previous analysis indicating the benefits of the latter phase of the tax cuts flow to high-income workers.

It says stage three of the package, outlined by the Coalition in the budget handed down before the election, will cost the budget $95bn over five years, and the bottom 20% of taxpayers will get 0.2% of the benefit of the proposed cut, with the bottom 10% of taxpayers receiving nothing at all.

Anticipating turbulence about the package once parliament resumes, the treasurer, Josh Frydenberg, has declared he will not split the bill.

Frydenberg says parliament needs to pass the whole package when MPs return in July for the first sitting post-election. In an interview with Guardian Australia last week, the treasurer said the package “must be supported in its entirety and as a priority”.

The treasurer is framing the tax relief as economic stimulus, pointing to global economic headwinds, coupled with pressures in the domestic economy, such as weak consumption and a slowdown in the housing market, as reasons to increase the spending power of Australian consumers to boost growth.

The Coalition and Labor agree on the first stage of tax cuts – worth a total $1,080 for people earning between $50,000 and $80,000 – but Labor has previously opposed stages two and three of the package.

The new Labor leader, Anthony Albanese, in his opening days in the job has signalled the opposition is still not inclined to support stage three of the plan given it would bake in tax relief several years down the track, which could be fiscally irresponsible when there is considerable uncertainty about the state of the economy.

But Albanese has left the door open on supporting stage two of the plan. Labor is yet to have any formal discussions about how to recalibrate the tax position post-election, so the landing point is not yet clear, but Albanese has signalled Labor needs to do more to appeal to aspirational voters.

The new leader said on Thursday that Labor in the coming term needed to appeal to people who are successful “as well as lifting people up”.

The executive director of the Australia Institute, Ben Oquist, argues there is an economic rationale for more immediate tax cuts for low and middle income earners that could stimulate the economy at a time of sluggish economic growth, but “there is little evidence” to suggest tax cuts for high income earners are needed on either economic or equity grounds.

Labor’s position may be irrelevant in a parliamentary sense, because the Centre Alliance senator Rex Patrick has offered the Coalition a lifeline, suggesting the minor party “would love to give hard-working Australians a tax cut” if it is confident income tax rebates will not cause cuts to services down the line.

Centre Alliance wants a briefing from Treasury to ensure that in a softening economy the tax cuts will not trigger cuts to health, education, aged care or pensioners in the future.