In parts of the United States, health officials have also seen a steady climb in the number of Omicron cases. The variant has been detected in at least 16 states: California, Colorado, Connecticut, Hawaii, Louisiana, Maryland, Massachusetts, Minnesota, Missouri, Nebraska, New Jersey, New York, Pennsylvania, Utah, Washington and Wisconsin.

Some Americans, too, are becoming more nervous.

“We’re paying closer attention, which we haven’t probably for a little while,” said Rory Bakke, who lives in Marin County, Calif. “It’s upped our attentiveness to the reports of symptoms and how contagious it is and the science reports.”

Ms. Bakke expressed frustration over the latest threat.

“I feel like if everyone had just followed the guidelines, we wouldn’t be in this situation,” she said. “So that’s disheartening.”

The Omicron variant was first identified in southern Africa in late November. On Saturday, Zambia became the latest African country — alongside South Africa, Botswana, Nigeria and Ghana — to report cases.

Since its emergence, a number of travel restrictions have been imposed to try to slow its spread, including in the United States and Europe.

Still, some European governments have been hesitant to impose sweeping new domestic restrictions ahead of a highly anticipated period of travel and big gatherings, especially given the lockdown in much of Europe last winter. Many have instead opted to focus on restricting travel from abroad or requiring more testing for travelers.