Labor has poured cold water on the proposal but has not ruled out reducing the 54 cents-a-litre fuel excise for the second time in fewer than six months, while stressing it has plenty of other cost relief measures left in its arsenal.
"That excise cut was temporary, we were very clear on that right from the beginning," energy minister Chris Bowen told ABC TV on Monday.
"We did extend it a bit to have it gradually return to more normal levels, that has played out, we're not going to respond to every daily movement on the world oil price."
After conflict between the US and Iran closed the Strait of Hormuz and sent oil prices skywards, the government cut the tax on fuel by 32 cents per litre for three months from April 1, when a litre of petrol cost $2.32 and diesel $2.75 on average in capital cities.
The levy was brought back in 16 cents-a-litre increments, returning in full by August 2 after a ceasefire calmed global oil markets.
That agreement is now in tatters, with missiles continuing to fly across the Gulf, multiple planned peace talks binned, and the Strait effectively closed.
Iranian-backed Houthi rebels have also seized key strategic islands in the Red Sea, another major trade route, allowing them to target Saudi Arabian oil shipments previously untouched by the conflict and further complicating the the regional chaos.
A litre of fuel has now crept above $2 a litre in all capital cities, and diesel about $2.50, according to the latest monitoring by the consumer watchdog.
Mr Bowen reiterated the government had no immediate plans to reach for a second excise cut.
"It's not the only cost of living measure that we put in place," he said.
"Tax cuts, cheaper medicines, free TAFE, right across the board, and so we'll obviously continue to focus on those other measures."
Mr Bowen will travel to Saudi Arabia in the coming days to receive an update on the situation from the kingdom's energy minister.
Australia has 41 days worth of petrol, 32 days of diesel, and 30 days of jet fuel, per the minister's latest update on September 12.