"We have just come too far, we've lost too many loved ones, we've already sacrificed far too much to ease up now, especially when we are beginning to see the evidence that our efforts are starting to pay off," Raab told reporters.
Raab is deputising while Prime Minister Boris Johnson recuperates from Covid-19 complications that nearly cost him his life.
Raab chaired an emergency meeting on Thursday to review scientific evidence on the impact of the existing lockdown "Based on this advice... the government has decided that the current measures must remain in place for at least the next three weeks," he said.
"Relaxing any of the measures currently in place would risk damage to both public health and the economy."
The United Kingdom has the fifth-highest official death toll from Covid-19 in the world, after the United States, Italy, Spain and France, though British figures only cover hospital fatalities and the real number is probably much higher.
The UK has 103,093 cases and 13,729 people have died.
The announcement, which had been widely expected, means Britons must stay at home unless they are shopping for basic necessities, or meeting medical needs. Citizens are allowed to exercise in public once a day, and can travel to work if they are unable to work from home.
The measures were announced on March 23 for an initial three-week period. Medical advisers speaking alongside Raab said they had reduced the overall rate of transmission of the virus to below 1, meaning it was now shrinking in the community.
Earlier, Health minister Matt Hancock warned the virus would "run rampant" if restrictions were lifted too soon.
Raab set out five loose conditions which must be met for the lockdown to be lifted.
But he refused to discuss any possible timeline - despite a growing political clamour for an 'exit strategy' to the most severe restrictions on daily life in British peacetime history.
Opposition Labour Party leader Kier Starmer said he supported the extended restrictions, but added: "We also need clarity about what plans are being put in place to lift the lockdown when the time is right."
A YouGov poll conducted before Thursday's announcement showed 91 percent of Britons supported a three-week extension to the lockdown.