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Boris Johnson has said a "psychological transformation" in his character is "not going to happen" after Tory by-election defeats led to calls for change.
The PM was asked to respond to Tory party chairman Oliver Dowden saying it could not be "business as usual" as he quit.
Mr Johnson told the BBC he "humbly and sincerely" accepts the criticism he is facing.
But speaking on Radio 4's Today programme he said he had to distinguish between "criticism that matters and what doesn't".
And Mr Johnson said that voters were "fed up of the conversation being about me".
Speaking from the Commonwealth heads of government meeting in Rwanda, he repeatedly said that policy was more important than allegations about his conduct.
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.
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.