Sir Keir Starmer has pressed Boris Johnson on the effectiveness of the NHS test and trace system in England, during Prime Minister’s Questions.
The Labour leader said it was a “big problem” that just over 10,000 people with coronavirus had been reached, despite estimates of 33,000 cases.
But Mr Johnson criticised Sir Keir for not supporting government actions.
The PM also dismissed questions about the tracking app for those who come into contact with the virus.
Sir Keir began his questioning by saying Labour supported the government’s announcement on Tuesday to ease more lockdown restrictions in England from 4 July.
But he said for it to work safely “we need an effective track, trace and isolate system”.
He added: “The prime minister promised a world-beating system would be in place by 1 June.
“I do recognise the hard work that has gone into this, but if two thirds of those with Covid-19 are not being reached and asked to provide contact details, there is a big problem, isn’t there?”
Mr Johnson claimed Sir Keir had been “stunned by the success of the test and trace operation”, adding: “Contrary to his prognostications of gloom, it has got up and running much faster than doubters expected.”
He said 87,000 contacts of those who tested positive for coronavirus had been reached, and called for his counterpart to “pay tribute” to the team working on the system.
But Sir Keir accused the prime minister of “not addressing the question”.
The Labour leader said the number of people who weren’t reached meant a “big gap” was in the system, adding: “The prime minister risks making the mistakes he made at the beginning of the pandemic – brushing aside challenge, dashing forward and not estimating properly the risk.”
Mr Johnson accused Sir Keir of “inadvertently giving a false impression of what test and trace is doing”, claiming it is contacting “the vast majority of those who test positive and their own contacts and getting them to isolate”.
He called it a “formidable achievement”, and said Labour was “yo-yoing back into a position of opposition”.
Sir Keir reiterated his support for lockdown easing, but said the PM was “wrong to reject challenge”, adding: “65,000 people have lost their lives because of Covid-19. The prime minister should welcome challenge that could save lives rather than complaining about it.”
The Labour leader also questioned the PM about when a mobile phone app to track people who had been in contact with others carrying the virus would be up and running.
He said it was the “only way of tracking unknown contacts”, such as people on beaches or in a park, who had been in close contact with one another.
The Labour leader quoted Health Secretary Matt Hancock – who called the app “critical” in May, but later said it was “only ever additional support” – asking the PM, “Which is it?”
Mr Johnson said there was “not a single country in the world that has a functional contract tracing app”, but England’s test and tracing system was working.
Sir Keir said Germany had a working app with 12 million downloads, before pushing the prime minister on a number of delays to the app and its cost of £12m.
“Other countries are ahead of us,” he said. “When are we going to have a working app?”
The PM said his opposite number was “completely wrong” about Germany, and said the government had “always been completely clear that the app was the icing on the cake”.
He concluded: “What we do have is a fantastic NHS test and trace operation that is already up and running, that is going to get better and better, and will be indispensable to our future success.”