The Prime Minister drew cheers from his Tory colleagues after his jibe against the Labour leader, who he claims is unable to take one stance on key issues.
Sir Keir had said Mr Johnson is "kidding no-one" by claiming everything is a "stunning success" in the Government’s Covid-19 response and urged the Prime Minister to acknowledge there are problems.
Speaking at PMQs, Mr Johnson said Sir Keir should help "build up the confidence" of the people of the country to "cautiously" get back to work and restart the economy instead of “endlessly knocking” their confidence.
Sir Keir hit back: "It’s perfectly possible to support track and trace and point out the problems, and standing up every week and saying it’s a ‘stunning success’ is kidding no-one – that’s not giving people confidence in the system.
"They’d like a Prime Minister who stands up and says, ‘there are problems and this is what I’m going to do about them’. Not this rhetoric about stunning success when it’s obviously not true.”
Mr Johnson defended the Government’s response, adding: "One day he [Starmer] says it’s safe to go back to schools, the next day he’s taking the line of unions; one day they’re supporting our economic programme, the next day they’re saying our stamp duty cut is an unacceptable bung; one day they say they accept the result of the Brexit referendum, the next day, today, they’ll tell their troops to do the exact opposite.
"He needs to make up his mind about which brief he’s going to take today because at the moment he’s got more briefs than Calvin Klein."
A spokesman for the Labour leader said after PMQs: “It tells you everything you need to know about the Prime Minister’s flippant approach to this crisis.
"Keir was raising very serious concerns from bereaved relatives and the Prime Minister responded with a pre-prepared joke."
Sir Keir also questioned the PM over whether the recommendations of the Government’s advisory group will be implemented in full, which detail the challenges posed this winter.
He said: "That report assessed the reasonable worst-case scenario for this autumn and winter including a second Covid spike and seasonal flu and it set out strong recommended actions to mitigate the risks.
"The report was clear July and August must be a period of intense preparation, i.e. now. Can the Prime Minister make clear he intends to implement the recommended actions in this report in full and at speed?”
Mr Johnson responded: “Not only are we getting on with implementing the preparations for a potential new spike, but he will know that the Government is engaged in record investments in the NHS.”
The PM went on to hail the UK’s Covid-19 test and trace system as being “as good as or better than” any other system in the world, although Sir Keir cast doubt on its success in ensuring people self-isolate.
Asked if he had read the advisory group’s report, Mr Johnson replied: “I’m of course aware of the report.”
Sir Keir also warned that the Government’s decision to not provide sector-specific support to those most at risk "could end up costing thousands of jobs" as he highlighted job losses across the aviation industry.
He pressed for British Airways to lose landing slots if it continues with plans to rehire workers on “worse” terms and conditions.
Mr Johnson offered assurances over the Government’s “huge” effort to help the sector but Sir Keir pressed: “Alongside the 12,000 redundancies already announced, BA is trying to force through the rehiring of the remaining 30,000 workers on worse terms and conditions.
“That is totally unacceptable and it is a warning shot to many other working people.”
He added: “Will the Prime Minister now personally intervene and make clear that actions like those at BA cannot be allowed to stand without consequences for landing slots?”
Mr Johnson said: “Let’s be absolutely clear, British Airways and many other companies are in severe difficulties at the moment and we cannot, I’m afraid, simply with a magic wand ensure that every single job that was being done before the crisis is retained after the crisis.
“What we can do and what we are doing is encouraging companies to keep their workers on with the Job Retention Scheme, with the Job Retention Bonus and with a massive programme in investing in this country, a £600 million investment programme in this country to build, build, build and create jobs, jobs, jobs.”