France is facing a worrying surge in cases, the government said on Friday, warning that the new cases were rapidly increasing and that hospitals were seeing an uptick in admissions.

Many expected new restrictions, especially after the government’s scientific council said earlier this week that the authorities would have to take “difficult measures.”

But the authorities did not announce new rules, vowing instead to improve the country’s massive testing program — which has been plagued by delays in recent weeks — and urging the French to continue social distancing measures.

The country registered about 54,000 new cases over the past 7 days — less than Spain, but far more than other neighboring countries like Italy or Germany. Nearly 31,000 people in France have died of the virus.

On Thursday, there were nearly 10,000 new confirmed cases, a record since the beginning of the epidemic. The surge is due partly to widespread testing, but the positivity rate for those tests has also increased — it was at 5.4 percent this week, up from 1.5 in late July — meaning that the virus is picking up speed.

Jean Castex, the French prime minister, said in a televised address on Friday that authorities were particularly worried about a renewed increase in the number of hospitalizations, especially of elderly people.

“This shows there is no Maginot line,” said Mr. Castex, referring to national fortifications built in the 1930s. Even if the virus is still mostly spreading among younger people, he said, it “inevitably” ends up reaching more vulnerable segments of the population.



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