The prime minister will declare the drive will help the UK meet its green targets “without adding undue burdens on households".
The government says the change will boost energy security, reduce dependence on “hostile foreign regimes” and give the industry long-term confidence.
But Sir Keir Starmer has said a Labour government would halt new licences. To overturn the latest changes a Labour government would have to bring forward its own legislation.
Energy secretary Claire Coutinho said: “As the independent climate change committee acknowledges, we will need oil and gas even as we reach net zero.
“It’s common sense to make the most of homegrown advantages and use oil, gas, wind and hydrogen on our doorstep in the North Sea.”
David Whitehouse, the chief executive of Offshore Energies UK, which represents the industry, said: “We should prioritise our production to support our energy security, our economy, our jobs, and our world-class supply chain that will be the foundation of our low carbon future.”
Mr Sunak sparked a furious civil war in the Tory party in September after he U-turned on key net zero pledges.
The prime minister announced that the 2030 ban on the sale of petrol and diesel cars – and gas boilers – would be pushed back to 2035. He also attacked climate “zealots” and said it was wrong to “impose such significant costs on working people”.
But former Tory prime minister Boris Johnson and ex-US vice-president Al Gore led the outrage against his watering down of climate promises.
Under the latest plans, each annual licensing round will take place only if key net zero tests are met. These include that the UK must be projected to import more oil and gas from other countries than it produces at home. Another important test will be that carbon emissions associated with the production of UK gas are lower than the equivalent emissions from imported liquefied natural gas, the government said.