Boris Johnson has said a “psychological transformation” in his character is “not going to happen” after by-election defeats led to calls for change.
The PM was responding to Tory party chairman Oliver Dowden saying it could not be “business as usual” as he quit.
Mr Johnson told BBC Radio 4’s Today programme, he “humbly and sincerely” accepts criticism.
But he said he also had to distinguish between “criticism that really matters and criticism that doesn’t”.
The by-election defeats in Wakefield and Tiverton and Honiton on Friday came after the prime minister faced months of criticism over parties in Downing Street during lockdown, alongside soaring inflation and a narrower-than-expected win in a confidence vote from his own MPs.
Speaking from the Commonwealth heads of government meeting in Rwanda, Mr Johnson repeatedly said that policy was more important than allegations about his conduct.
Mr Johnson said voters were “fed up with hearing conversation about me” and wanted to focus instead on the cost of living, the economy and “standing up to violence and aggression” in Ukraine.
The PM was challenged by presenter Mishal Husain that a lot of the criticism had been about him personally and had come from people who had worked with him.
They included his top policy aide Munira Murza, who criticised Mr Johnson’s “scurrilous allegation” about Jimmy Savile and Sir Keir Starmer; former minister Jesse Norman, who said the PM “presided over a culture of casual law-breaking”; and ethics adviser Lord Geidt.
But Mr Johnson said: “As a leader, you have to try to distinguish between the criticism that really matters and the criticism that doesn’t.”
Asked if there was any matter of principle he would consider resigning over, he said if he had to abandon Ukraine because it became too difficult or the costs were too great, he would quit.
He said that “of course” he regarded morality as a part of leadership.
But Mr Johnson was questioned about how he had not resigned over misleading the House of Commons, breaking the law for the Covid fine, or losing the support of 41% of his MPs in the confidence vote.
“Let’s look at this in a more cheery way, if that’s possible” he said. “Actually, what’s happened is that I’ve got a renewed mandate from my colleagues, and I’m going to continue to deliver.”
The prime minister did not engage with a question about the UK’s top civil servant Simon Case having an informal conversation about job opportunities for his wife, Carrie.
“The worst thing I could do is get into conversations about my family,” he said.