The fuel excise was cut by 32 cents a litre three months ago following the outbreak of war in the Middle East and ensuing strangulation of global oil supplies.
A tentative truce this week has allowed cargo ships to resume transiting more freely through the Strait of Hormuz, but the loss of fuel supplies triggered by hostilities could take months to recover.
How long the waterway stays open remains unclear.
Asked whether the government was any closer to a decision on prolonging the excise relief, the prime minister was coy.
"We'll be making a decision over the coming days about that and we'll announce it appropriately," he told reporters in Sydney on Saturday.
The response was identical to the one he had offered the Canberra press gallery six days earlier.
The excise cut is scheduled to expire on June 30, by which time it will have cost the federal budget an estimated $2.9 billion in foregone revenue.
Pushed on whether he was concerned a call on extending the discount might re-trigger demand issues, Mr Albanese said he hoped not.
"I think people will continue to behave responsibly," he said.
"It wasn't helpful that ... prior to Easter and around that period, we had very alarmist comments from members of the opposition and that was echoed by some through media channels and that people were concerned about whether they would be able to get out and about."
Energy Minister Chris Bowen said Australia currently had 44 days' worth of petrol in reserve, or about eight days more than when the US first bombed Iran in late February.
 Diesel stocks are running at 39 days and jet fuel at 32 days.
"Last week was the highest level of fuel held in Australia since the minimum stock obligation came into force in 2023," Mr Bowen said.
"This week is the second highest at 6.3 billion litres."
There are 51 fuel tankers on the water and headed to Australia, with 3.9 billion litres of fuel contracted for delivery in the next month.
Despite the de-escalation in fighting in Iran, Mr Albanese said a great deal of uncertainty still surrounded the resumption of normal trade.
"We do note there has been a considerable decrease in the price of oil in this week since the announcement by the United States and Iran," he said.
"But with regard to the volatility, which is still there, we've said the whole way along that there would be a long tail to the economic impact of this."
Mr Albanese said he spoke to fuel company executives most days and would continue to closely monitor the situation, particularly regarding regional demand for supplies.
According to the Australian Competition and Consumer Commission, average capital city bowser prices for petrol are hovering between $1.65 and $1.92 per litre.
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