The prime minister insisted he was up to the challenge of fighting off Tory rebels who want him replaced, laughing at the idea that some of his MPs were scheming against him.
And with the Conservatives trailing badly in the polls, Mr Sunak held up the prospect of a cut in national insurance before the next election to woo voters.
“I believe hard work should be rewarded,” he said in an interview with The Times. “Cutting national insurance is a very direct way to do that.”
Last month the Institute for Fiscal Studies warned against early tax cuts, saying they risked leading to tax rises or spending cuts later on, and the International Monetary Fund agreed. Chancellor Jeremy Hunt had vowed to cut taxes in his spring Budget.
The PM has faced crisis after crisis this year, as the Tories have descended into open infighting.
Former cabinet minister Sir Simon Clarke tried to have him ousted as leader, warning said the Tories would be “massacred” at the election without a new leader. But Tories lashed out at the “foolish” and “facile” move, while ex-defence secretary Ben Wallace warned it was “division and another PM [that] would lead to the certain loss of power”.
His coup attempt came after an anonymous group of Tory donors funded a poll suggesting he was leading his party to electoral oblivion.
The prime minister faced suspicions of more attempts to remove him just two weeks ago, when it emerged Kemi Badenoch - a future leadership favourite - and housing secretary Michael Gove were reported to both be members of a Tory WhatsApp group called Evil Plotters.
This week, Mr Sunak’s leadership rival Liz Truss attempted to restart her political career with the launch of a new right-wing Tory faction, called Popular Conservativism.
The shortest-serving prime minister in British history took a swipe at his government for allowing people to choose their gender and for “pandering to the anti-capitalists”.
She said Britons wanted lower immigration and wanted illegal immigrants deported, but efforts were “constantly being stymied”.
Asked about people in his own party plotting against him, Mr Sunak told The Times: "I'm totally up for the fight."
Mr Sunak’s flagship Rwanda bill, which allows asylum-seekers to be deported to the African country, has faced significant hurdles going through parliament and has attracted huge opposition. It suffered a major rebellion from his colleagues, with 60 of his MPs signing amendments.
Even if the bill passes, it is likely deportations will face legal challenges as migrants are prepared for removal.
But the prime minister hinted at future efforts to try to rewrite the European Convention on Human Rights, telling The Times there was a “growing consensus” that it needed reform.
“Everyone is looking at different solutions because this is becoming a growing problem,” he said. “On this we are showing leadership and hopefully people can see that what we’re doing is right. Everyone recognises this is not a sustainable situation and it requires novel solutions to fix.”