Boris Johnson has acknowledged that the government’s defeat in two by-elections were not “brilliant results” – but insisted he was not worried about Conservative MPs plotting to replace him while he’s abroad.

The prime minister was speaking at a press conference in Rwanda hours after the Liberal Democrats overturned the Tories’ 24,000 majority to win the Devon seat of Tiverton and Honiton, while Labour took back the red wall constituency of Wakefield in Yorkshire.

Mr Johnson told reporters in Kigali: “I’m not going to pretend these are brilliant results.”

“We’ve got to listen, we’ve got to learn,” he said, adding: “When people are finding it tough, they send messages to politicians and politicians have got to respond – and that’s what we’re doing.”

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Asked if he was worried about Conservative colleagues plotting to replace him while he was abroad, the PM bluntly replied: “The answer to the question is no.”

But he dodged a question about whether he had considered resigning at any point today.

“If governments crumpled because of by-election results in the whole of the post-war period, we wouldn’t have had many post-war governments,” he added.

When Sky’s Beth Rigby asked why he would not “acknowledge you could be part of the problem with voters”, the PM said: “I genuinely, genuinely don’t think the way forward in British politics is to focus on the issues of personalities, whether they are mine or others.”

He said people “will continue to beat me up and say this or that about to attack me”, adding: “That’s fine. That’s quite right. That is the job of politicians.”

The poor performances overnight led to the resignation of Conservative Chairman Oliver Dowden, who told the PM: “We cannot carry on with business as usual.”

But Mr Johnson insisted he would stay on with his “historic mandate” from the 2019 general election.

Culture Secretary Nadine Dorries defended the prime minister, calling the results a “reminder that we must be relentless in cracking on with the job of delivering”.

She also claimed by-elections were “useless… as an indication of absolutely anything at all”, adding the government would “remain relentlessly focused” on delivering for the public.

But shadow levelling up secretary Lisa Nandy said there was “a lot of distaste” for the PM on the doorstep when Labour were campaigning in Wakefield.

She told Sky News that voters were “genuinely feeling that this is a government that simply isn’t working”.

However, she said the “storming result” for her party was not just “people turning away from the Tories”, but constituents “looking towards Labour again”, and its leader, Sir Keir Starmer.

Education Secretary Nadhim Zahawi said the Conservatives “need to listen” to its voters, especially those who stayed at home, adding: “We need to give them reasons to come back at the next election. We do that with a laser-like focus on delivery.”

But he felt short of explicitly backing Mr Johnson, adding: “The voters will judge this Conservative government on what we deliver next. For me, it’s a focus on skills, schools and families.”