LONDON — British Health Secretary Matt Hancock said Wednesday that people who do not have symptoms of the novel coronavirus should not request tests.

About 25 percent of those seeking swabs were “not eligible,” he said, which places undue strain on the overloaded testing system.

The comments sparked confusion in Britain, which has the highest death toll in Europe, about testing for asymptomatic people. Several opposition Labour Party lawmakers pointed out that health officials had, in recent days, blamed young and often asymptomatic people for spreading the virus over the summer.

“If you don’t have symptoms, unless asked specifically to get a test, you’re not eligible for a test,” Hancock said in an interview with the BBC, adding that he had heard reports about entire schools asking for tests, a demand that he said was not appropriate.

“We’ve got to be firmer, I’m afraid, with the rules around eligibility for testing,” he said. He did not say to what extent the recommendation was informed by a simple lack of available tests in the country, where people regularly have to travel up to 100 miles to receive swabs — even if they are experiencing symptoms.

The debate over testing for those without symptoms is not confined to Britain.

Last month, the U.S. Centers for Disease Control and Prevention, which had once urged everyone to be tested for the virus even if they were not displaying symptoms, changed its policy, saying people without symptoms “do not necessarily need a test.”

The CDC now advises vulnerable people who think they have been within six feet of an infected person for at least 15 minutes to seek a test, along with those experiencing symptoms consistent with the coronavirus.

On Tuesday, directors at the National Institutes of Health published a blog post saying that testing “as many people as possible” is the key to helping slow the spread of the virus, CNN reported.

Some critics say the British government has sent mixed messages. At a news briefing in June, Hancock cited a report from Britain’s Office for National Statistics that found that an estimated 71 percent of people who tested positive for the infection in Britain did not experience any symptoms. At the time, Hancock said that the findings were “significant” and that the true figure could be higher.

In July, he advised testing if “you have symptoms,” or “if you have any doubt.”

Hancock’s remarks come as the British government moves to impose a “rule of six” — a ban on gatherings of groups of more than six people, both indoors and outdoors, starting Monday — in an effort to avert a second severe surge in infections.

Those found to be ignoring the new measures could face a 100-pound ($130) penalty, a fine that will double if the offense is repeated. The law will not apply to workplaces, weddings, funerals or schools. Many students returned to the classroom this week.

At a news conference Wednesday, British Prime Minister Boris Johnson doubled down on Hancock’s line on asymptomatic testing, but pledged 500,000 tests a day by October and the eventual expansion of testing to those without symptoms. He did not say how long the rule of six would remain in place.

More than 41,600 people in Britain have died of covid-19, the disease caused by the coronavirus, and this week the country recorded its highest infection rates since May. Confirmed cases are on the rise, particularly among younger people, in the country and across Europe.

On Monday, Jonathan Van-Tam, Britain’s deputy chief medical officer, said that people ages 17 to 21 were “lucky” that they were less likely to become sick or suffer from symptoms associated with the virus, but said they had the potential to be “potent spreaders” to others more at risk.

Keir Starmer, the leader of the Labour Party, called on Johnson to address the nation’s testing problem, saying that he was aware of hundreds of families being denied access to testing and home test kits, despite having symptoms.

“If they can’t get tests, the prime minister needs to take responsibility,” Starmer said.

Other Labour lawmakers voiced similar fears.

“My constituents are being told to travel hundreds of miles for a coronavirus test. Others can’t get one at all. Instead of taking responsibility for these serious issues with test and trace, Boris Johnson & Matt Hancock are blaming others,” Afzal Khan tweeted.

Labour lawmaker Tracy Brabin accused the government of creating “chaos” by blaming people seeking tests, rather than the lack of testing.

Johnson hit back at the criticism, saying on the floor of the House of Commons that the government was “working flat out to address all the issues confronting us today,” and hailed the efforts of testing staff.