The Queensland government says drilling the Taroom Trough, about 480km northwest of Brisbane, is a "generational opportunity".
Premier David Crisafulli wants federal Environment Minister Murray Watt to use his discretion to grant a national interest exemption in response to the fuel crisis.
"Never again should we be left without the ability to generate domestic fuel supply," Mr Crisafulli said in a statement.
"This is a generational opportunity to ensure we're not left at the end of a global supply chain.
"Unlocking the Taroom Trough is critical to locking in future national fuel security."
Shell already produces around 200 barrels of oil per day from the site, about 480km northwest of Brisbane.
The fuel is then trucked to Eromanga in southwest Queensland for refining to diesel.
Approval would be required under the Environment Protection and Biodiversity Conservation Act to scale up production at Taroom.
However, Mr Watt said it was not possible to exempt a fossil fuel project from the EPBC Act, even via a national interest exemption.
"There are other ways to simplify approvals for oil and gas projects," he said in a statement to AAP.
"We would be happy to consider any concrete proposal the Queensland government puts forward - we have yet to receive anything from them."
Earlier, Mr Crisafulli suggested the act should be amended after landmark reforms were passed in December.
"The fact that the development of the fuel industry wasn't included in that at that time, it was a very different paradigm," Mr Crisafulli told the ABC.
"There is nothing more in the national interest at the moment, it's the one thing that people are talking about and justifiably, because we have seen how exposed we are."
But federal Energy Minister Chris Bowen said Commonwealth approval would be based on economics and engineering, and the project would have to go through the normal process.
"Obviously, it has to stack up economically," he said, in a debate with opposition spokesperson Ted O'Brien at the National Press Club.
He denied the EPBC Act needed to be changed in light of the war in Iran and the subsequent crisis in oil supply.
"There are things that can be done with the Queensland government and the Commonwealth government working together on a bilateral agreement to fast-track approvals," he said.
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