The UK government has also said it will support a carbon capture project in the north east of Scotland.
Campaigners said that extracting more fossil fuels from the North Sea would “send a wrecking ball through the UK’s climate commitments”.
But Mr Sunak said granting the new licences was “entirely consistent” with net zero commitments.
It comes as the party faces internal divisions over its green policies – such as the review over low-traffic neighbourhoods in England – with some MPs calling for a rethink.
Mr Sunak confirmed support for the Acorn Project in St Fergus, Aberdeenshire, on the BBC’s Good Morning Scotland programme, then later visited the site.
It is one of four carbon capture projects which will share up to £20bn of funding.
Mr Sunak said the announcement would support thousands of jobs across the UK.
He said granting the new oil and gas licences was “the right thing to do”.
He said: “Even when we reach net zero in 2050, a quarter of our energy needs will still come from oil and gas and domestic gas production has about a quarter or a third of the carbon footprint of imported gas.”
The prime minister also said it made “absolutely no sense” to import energy supplies with “two to three times the carbon footprint of what we have got at home”.
He said increasing home-grown sources of energy would improve the UK’s resilience, create jobs and generate tax revenue to fund public services.
Mr Sunak said the government was determined to transition to net zero in a “proportionate and pragmatic” way.
And he also defended his plans to fly to Scotland as “an efficient use of time for the person running the country” and highlighted investment in new technologies, such as sustainable aviation fuel.
The prime minister said: “If your approach to climate change is to say that no one should go on holiday, no one should go on a plane, I think you are completely and utterly wrong.”
The Acorn project in St Fergus in Aberdeenshire missed out, quite controversially, on track one of funding for this back in 2021.
Instead it went to two projects in the north of England.
That was highly controversial because there had been heavy hints placed that the Scottish project would form part of that.
It was one of the most advanced projects in the UK, if not the most advanced, and then suddenly it was dropped.
The accusation was that the Conservative government at Westminster was favouring Red Wall constituencies following its success at the last general election.
But it was always the case that this would be a sequencing of events.
Between the projects announced in 2021 and today 10 mega tonnes of carbon dioxide will be captured and stored by 2030, the UK government says.
That includes emissions from Mosmorran, from Grangemouth, from a new power station to be built at Peterhead and, potentially, from direct air capture.
It effectively sucks carbon dioxide out of the atmosphere and also stores it.
Labour’s Ed Miliband claimed the Conservatives’ energy policy had left Britain as “the worst hit country in Western Europe during the energy crisis”.
Mr Miliband, the shadow climate change secretary, said: “Rishi Sunak’s weak and confused policy will not take a penny off bills – as his own party chair has admitted – will do nothing for our energy security, and drive a coach and horses through our climate commitments, while continuing to leave us at the mercy of fossil fuel dictators like Putin.”
And Scotland’s First Minister Humza Yousaf said the new oil and gas licences demonstrated the UK government was “not serious about tackling the climate emergency”.
He tweeted: “For the PM to announce unlimited extraction of oil & gas, in the week the UN has confirmed July is set to be the hottest month in human history, shows the PM is willing to recklessly gamble the future of our planet for cheap political gain.”