The 32-cent-a-litre discount on petrol and diesel will be cut to 16 cents, from Wednesday before ending entirely at the start of August.
The measure has aimed to reduce petrol bill shock amid ongoing negotiations to end the Middle East conflict.
The closure of the Strait of Hormuz after US and Israeli strikes on Iran caused chaos on global oil markets and sent Australian fuel prices skyrocketing.
That shock to household budgets was much larger for people on lower incomes than it was for wealthier Australians, according to a report by the e61 Institute.
"Low-income households spend a much larger share of their incomes on petrol, meaning they are hit harder by price rises," economist Adit Maitra said.
The research found Australians are more sensitive to petrol and diesel price rises than previously thought, with a 10 per cent cost increase correlating with a 3.8 per cent fall in fuel consumption.
Scaling back the fuel excise would hit low-income households harder, but that did not mean the measure should remain in place, Mr Maitra said.
The excise cut was poorly targeted because it disproportionately benefited high-income households who used the most petrol, he said.
The federal government has defended its decision to reduce the amount of relief offered to motorists, arguing recent prices have been lower than they were before the start of the war.
"Our fuel excise cut is part of the story, but also we've seen some welcome developments in the Middle East playing out in global oil markets," Treasurer Jim Chalmers told reporters on Tuesday.
"We've gone for this very responsible, targeted, temporary, tapered extension to the fuel excise cut for good reason," he said.
Petrol prices were expected to rise in the coming week from their lowest level since October 2021, but the immediate impact had been cushioned somewhat by falling global oil prices, the NRMA said.
The consumer watchdog has warned fuel retailers not to use the excise to jack up profits and has encouraged motorists to shop around for the best price.
US and Iranian officials are heading to Qatar's capital Doha but there are conflicting reports about whether the two sides will meet to discuss a potential peace deal.
US President Donald Trump says his country is winning the war militarily and insists Iran must not be allowed to produce a nuclear weapon.
While both sides have agreed to a ceasefire, America has accused Iran of attacking at least two commercial ships attempting to pass through the Strait of Hormuz in recent days.
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