Governors urge caution in the United States on the Omicron variant.

On Friday, Gov. Kathy Hochul of New York declared a state of emergency partly in response to the emerging Omicron variant of the coronavirus. Most governors did not comment publicly on the threat over the weekend, but some said they were monitoring developments without taking any new steps.

Gov. Ned Lamont of Connecticut issued a statement on Sunday saying local health officials were paying close attention to the Omicron variant.

“Our team at the Connecticut Department of Public Health, led by Commissioner Manisha Juthani, is following these developments closely,” he said in the statement. “While there have been no cases of the Omicron variant reported here in Connecticut or the United States to date, we still must be vigilant. Given the number of countries where Omicron has already been detected, it may already be present in the U.S.”

Other state leaders took the same tone, urging caution as well as highlighting the resources they had already put in place through the pandemic.

Mr. Lamont pointed to the network of labs sequencing genomes in his state and reminded residents to wear masks in indoor public spaces.

Gov. Gavin Newsom of California said on Twitter on Sunday that the state was “monitoring the new variant from Southern Africa closely.” He did not announce any new steps but said that the coronavirus vaccine and booster shot were essential.

The Los Angeles County Department of Public Health echoed that message and said in a statement, “More studies are needed to determine whether the Omicron variant is more contagious, more deadly or resistant to vaccine and treatments than other Covid-19 strains.” The department added that people in Los Angeles should adhere to existing mask requirements.

“While we are still learning much about Omicron, we know enough about Covid to take steps now that can reduce transmission as we prepare to better understand the additional strategies that may needed to mitigate this new variant of concerns,” the statement said.

Health leaders in the United States have said that it is all but inevitable that the variant will reach the country and called this a time for caution but not panic.

“We’re going to get better information about this,” Dr. Francis Collins, director of the National Institutes of Health, said on the CNN program “State of the Union.” “But there’s no reason to panic. But it is a great reason to go get boosted.”

Some leaders sought to reassure residents. Gov. Dan McKee of Rhode Island said that its health department was not aware of any cases in the state linked to the variant, although he said that the state would continue to be on the lookout.

“The best way to keep RI safe: Get vaccinated. Get your booster,” he said on Twitter.

On Saturday, his office issued a statement to the Providence-based news outlet GoLocalProv, saying that the state’s health laboratories already perform genomic surveillance on samples, “which would identify the Omicron variant.”

In New York, under Ms. Hochul’s executive order, all state agencies are authorized “to take appropriate action to assist local governments and individuals” in containing and responding to cases. Although the measures are a far cry from early pandemic rules, they were the nation’s first attempt to accelerate preparation for the arrival of Omicron.

“We continue to see warning signs of spikes this upcoming winter, and while the new Omicron variant has yet to be detected in New York State, it’s coming,” Ms. Hochul said in a release.

Two governors of more conservative-leaning states addressed concerns about the variant, too, but maintained their position that vaccine mandates were off the table for now.

Gov. Asa Hutchinson of Arkansas said on “State of the Union” that while a new variant “is a great concern,” encouraging vaccinations would work better than forcing them.

Gov. Tate Reeves of Mississippi made similar statements on NBC’s “Meet the Press.” “We’re certainly monitoring this new variant,” he said. “We don’t have all the data that we need to make decisions at this time.”