“All indicators suggest the country may have passed the peak of the fourth wave at a national level,” South Africa’s minister in the presidency Mondli Gungubele said Thursday, citing declining Covid-19 cases and hospital admissions. The government lifted a curfew and restrictions on alcohol sales ahead of New Year’s Eve, though mask-wearing orders and limits on gatherings remain in place.

Omicron’s rapid decline in South Africa offers hope to other countries that they, too, can weather surges in cases. The variant, first detected by South African scientists in November, has driven recorded infections to new highs in countries including the U.K. and France and prompted many governments to tighten public-health measures to limit hospitalizations.

Though the South African data is encouraging, scientists caution that the country’s experience might not be repeated in Europe, the U.S. and other countries grappling with Omicron. South Africa’s population is young and likely has some degree of immunity to severe disease with the variant because of high levels of prior infection. It is also summer in the Southern Hemisphere, and the virus tends to spread more easily in winter, when people are huddled indoors.

Still, another encouraging sign is coming from a growing body of evidence suggesting the variant is causing milder illness, especially in those with a degree of immunity from vaccination or prior infection.

New analysis published Friday of more than half a million confirmed or possible Omicron cases in Britain by the U.K. Heath Security Agency found the overall risk of hospitalization with the variant was around a third of the risk associated with the earlier Delta strain, after adjusting for risk factors including age, sex and vaccination status.

The agency found that vaccines provide substantial protection against severe illness with Omicron, especially after a booster shot. In one analysis, three doses of vaccine reduced the risk of hospital admission by 81% compared with the risk faced by unvaccinated people; a second analysis of a smaller group of cases put the reduction in risk at 88%.

Scientists and public-health officials say despite the reduction in the risk of severe illness, the speed at which Omicron spreads means it can still put substantial numbers of people in the hospital.

A week of record-breaking Covid-19 case reports in the U.S. saw the nation reach a new high on Thursday, with more than 647,000 infections reported and hospitalizations continuing to tick higher.

Thursday’s data—the largest number of cases recorded by the nation in a day—increased the seven-day average of reported daily cases to 355,991, according to a Wall Street Journal analysis of Johns Hopkins University data. That is about 104,000 more than the peak reached during last winter’s surge.

The surge is widespread, with 49 states and Puerto Rico reporting a seven-day average of daily cases that was higher than the 14-day average, which indicates reports of cases have accelerated.

Data collected by South Africa’s department of health recorded a 30% decline in the number of new Covid-19 cases in the week ended Dec. 25, compared with the previous week. Cases fell to 89,781, from 127,753. Hospital admissions declined in all provinces except the Western Cape, the government said.

A new analysis of South African hospital data, published on the website of the Journal of the American Medical Association, showed markedly less severe disease during the Omicron wave compared with previous surges of Covid-19. The analysis of data from Netcare, a private healthcare group, found 41% of patients arriving at emergency departments with Covid-19 symptoms were admitted to hospitals, compared with almost 70% in previous waves. Fewer patients needed oxygen or intensive care, the analysis found, though the authors said that those admitted tended to be younger and healthier than in previous waves.

“While the Omicron variant is highly transmissible, there has been lower rates of hospitalization than in previous waves. This means that the country has a spare capacity for admission of patients even for routine health services,” the government said in explaining its decision to ease restrictions.

In Europe, by contrast, the German government is preparing to unveil new measures to combat rising infections of the Omicron variant after the holidays. It has warned that current data significantly understate the actual number of infections.

The country’s Robert Koch Institute said Thursday that since mid-November 16,748 infections with the variant had been registered in Germany and five deaths reported.

“The actual incidence is probably two to three times higher than what we are actually measuring right now. In addition, we are worried about the significant rise in Omicron infections that we are seeing,” German Health Minister Karl Lauterbach said. He urged the public to exercise caution and restraint on New Year’s Eve and avoid large gatherings. Germany has banned fireworks to restrict large gatherings and prevent a flood of injured revelers clogging hospital emergency rooms.

In the Netherlands, a Covid-19 lockdown imposed on Dec. 19 helped push down average daily hospital admissions over the seven days through Dec. 25 to 167, from 323 at the start of the month. Hospital beds occupied and admissions to intensive-care units have also trended down.

In Israel, which is also seeing rising cases linked to Omicron, the government began rolling a fourth vaccine shot to immunosuppressed people and the elderly to shield the most vulnerable from illness.

“The greater the wave, the greater the protection we will need to overcome it,” said Prime Minister Naftali Bennett.

Israel’s Health Ministry recorded 4,916 new cases of the coronavirus on Thursday, more than double the caseload the country recorded on Sunday, and experts expect serious cases to increase into the thousands in a month from just fewer than 100 currently.

Earlier this week, Israel’s Sheba Medical Center began distributing a fourth vaccine to 150 medical personnel in a trial aimed at helping understand the implications of starting a fourth jab for the elderly and immunosuppressed.

—Aaisha Dadi Patel, Daniel Michaels and Anthony DeBarros contributed to this article.

Write to Jason Douglas at jason.douglas@wsj.com, William Boston at william.boston@wsj.com and Thomas Grove at thomas.grove@wsj.com

Corrections & Amplifications
The number of infections of Omicron in Germany was 16,748 since mid-November. An earlier version of this article incorrectly said there were 16,478. (Corrected on Dec. 31)