At prime minister's questions in parliament, the opposition Labour leader Keir Starmer suggested both systems were not yet ready before England eases its coronavirus lockdown from July 4.
"We have a very effective cluster-busting operation which is designed to ensure that we keep those outbreaks under control," Johnson said in his response, challenging Starmer to find any other country that has a functioning tracing app.
Starmer pointed immediately to Germany, which has had a large number of people downloading its app. Other countries have also launched their own tracing apps, such as Singapore, South Korea, and Italy.
The test-and-trace program is key to reopening the country but has been dogged by problems. A smartphone COVID-19 test-and-trace app developed by the National Health Service was initially expected to be rolled out nationwide in May but did not materialise.
Figures released last week of England's test-and-trace showed that while over 85,000 people who had tested positive for the new coronavirus had been reached in the first two weeks, over 25% of positive cases could not be reached.