An "IT failure" within Public Health England - reported to be a problem with an Excel spreadsheet reaching its maximum size - has been blamed by ministers for a delay in the reporting of 15,841 COVID-19 cases in England.
Downing Street revealed extra contact tracers had now been drafted in to help track down the contacts of people whose positive tests went unreported between 25 September to 2 October.
Meanwhile, a Whitehall investigation has been launched to disover why the missed cases were not identified sooner.
But the prime minister was said to still have full confidence in Baroness Harding, the head of the NHS Test and Trace programme.
Mr Johnson was quizzed about the glitch on Monday, with Labour having accused the government of overseeing a "shambolic" system.
Mr Johnson did not give an answer when asked how many people weren't traced, but who should have been, by NHS Test and Trace due to the delay in reporting the infections.
"I can't give you those figures," he said.
"What I can say is all those people are obviously being contacted and the key thing is that everybody - whether in this group or generally - should self-isolate.
"That's the way to make it work."
The prime minister said a successful use of the NHS Test and Trace scheme should create a "fire break" around an incidence of infection and "helps us fight the virus".
Referring to the technology error, Mr Johnson claimed that "some of the data got truncated" and "was lost".
According to the Press Association, the master Excel spreadsheet reached its maximum capacity so could not keep adding further cases.
Officials said that "rapid mitigation" measures have been put in place to make sure it does not happen again.
Mr Johnson added: "What they have done now is not only contacted all the people who were identified as having the disease - that was done in the first place - but they are now working through all the contacts as well."
Following the addition of the new COVID-19 cases to England's figures, the weekly rate of infections has soared in dozens of areas.
Earlier on Monday, Work and Pensions Secretary Therese Coffey was asked whether others might have been infected with COVID-19 due to the NHS Test and Trace scheme not being aware of the nearly 16,000 cases
"There may well be," she told Sky News.
"I've been made aware that probably the majority of that [contact-tracing] has happened in the latest element of the week, in the last couple of days.
"So it's important that we act quickly, and PHE is acting quickly, to see whether or not people are required to self-isolate.
"Because I do recognise that not quite everybody going through the regime will be identified by the test and trace regime to undertake that further self-isolation."
Asked whether the government would be issuing an apology over the issue, Ms Coffey pointed towards Health Secretary Matt Hancock's expected appearance in the House of Commons later on Monday.
In an earlier broadcast interview, Ms Coffey was unable to say how many close contacts of coronavirus cases were not contacted because of the system failure.
"I'm afraid I just don't have that information," she told BBC Breakfast.
Asked if they have now been contacted, she said: "I know that people who had the initial results have all been contacted, I don't know the answer to that question."
Labour MP Bridget Phillipson, the shadow chief secretary to the Treasury, accused ministers of overseeing a "shambolic" system.
"Test, trace and isolate just isn't working," she told Sky News.
Fellow Labour frontbencher Lucy Powell, the Manchester Central MP and a shadow business minister, said it was "very concerning" that infection rates had been revised upwards in Greater Manchester following the discovery of the computer glitch.
"Local understanding of what lies behind this increase is critical before we see ever more stringent restrictions imposed on us," she posted on Twitter.
"We've already been living under local restrictions longer (over 2 months) than most places."
Public Health England said on Sunday the people involved all received their test results and those who tested positive were advised to self-isolate.
Joint medical director Dr Susan Hopkins told Sky News: "There's no delay in people receiving their test results.
"The delays are in reporting to the dashboard and to the public and there's been a delay in contact tracing initiation.
"Public Health England apologise that this occurred and have put in place steps to prevent this happening again."