▶ Watch Video: U.S. prepares to fight Omicron COVID variant as new travel restrictions set to take effect

At least 32 cases of the Omicron COVID-19 variant have been reported across 12 states — 7 cases in California, 1 in New Jersey in a Georgia resident, 1 in Utah, 2 in Colorado, 1 in Missouri, 1 in Pennsylvania, 3 in Maryland, 6 in Nebraska, 1 in Hawaii, 8 in New York, 1 in Minnesota and 1 in Massachusetts.

The biggest question is whether current, available vaccines will prevent severe cases spread by the Omicron variant.

So far, the handful of known cases in the U.S. have been reported by health officials as mild and in vaccinated people. But with so few cases, there’s not enough evidence yet on what to expect from Omicron.

It’s still cases from the Delta variant that have officials’ attention, Tom Hanson reports for “CBS Saturday Morning.”

COVID cases driven by the Delta variant are rising, averaging 96,000 new cases a day and hitting hard in the Upper Midwest to New England. New Hampshire led the country in new cases per capita last week

“99.9% of cases in the country right now are from the Delta variant,” said Dr. Rochelle Walensky, director of the Centers for Disease Control and Prevention.

When it comes to the Omicron variant, health officials are counseling calm.

“We are equipped and prepared to fight the Omicron variant head on,” Walensky said.

“There’s every reason to believe that if you get vaccinated and boosted, that you would have at least some degree of cross-protection, very likely against severe disease, even against the Omicron variant,” said Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases and chief medical advisor to the president.

But Omicron spreads twice as fast as the Delta variant, and this week, mild cases of the strain, first identified in South Africa, popped up in multiple states including Maryland, where Governor Larry Hogan had just announced an aggressive partnership to find COVID cases fast.

“The state entered into agreements with both Johns Hopkins and the University of Maryland to more than double our already aggressive real-time variant surveillance,” he said this week.

International travelers will be required to take a COVID test one day before boarding a flight to the U.S. from a country where Omicron has been detected. Once they arrive, many airports have on-site testing.

More than two dozens countries have identified cases with the Omicron strain.

“Now is not the time to relax,” said Baltimore City Health Commissioner Dr. Letitia Dzirasa. “We’re seeing this variant of concern and the way to address variants is to slow COVID transmission, and we do that through vaccination, we do that through masking.”

Alexander Tin contributed reporting to this article.