Dining at restaurants and the lack of mask mandates are each linked to the spread of the virus in the U.S., the C.D.C. says.

As officials in Texas and Mississippi lifted statewide mask mandates, researchers at the Centers for Disease Control and Prevention offered, in a new study on Friday, fresh evidence of the importance of mask use. Wearing masks, the study reported, was linked to fewer infections with the coronavirus and Covid-19 deaths in counties across the United States.

The researchers also found that counties opening restaurants for on-premises dining — indoors or outdoors — saw a rise in daily infections about six weeks later, and an increase in Covid-19 death rates about two months later.

The study does not prove cause and effect, but the findings square with other research showing that masks prevent infection and that indoor spaces foster the spread of the virus through aerosols, tiny respiratory particles that linger in the air.

“You have decreases in cases and deaths when you wear masks, and you have increases in cases and deaths when you have in-person restaurant dining,” Dr. Rachel Walensky, the director of the C.D.C., said on Friday. “And so we would advocate for policies, certainly while we’re at this plateau of a high number of cases, that would listen to that public health science.”

The findings come as city and state officials nationwide grapple with growing pressure to reopen schools and businesses amid falling rates of new cases and deaths. Officials have recently allowed for limited indoor dining in New York City. And on Thursday, Connecticut’s governor said would be ending capacity limits later this month on restaurants, gyms and offices. Masks remain required in both places.

Coronavirus cases and deaths are down significantly across the country compared to the devastating peaks around the holidays. But as more cases of worrisome virus variants have been detected and the U.S. vaccination campaign continues, President Biden and his team have stressed in recent days that now is not the time for Americans to relax, particularly on wearing masks.

According to a New York Times database, the seven-day average of new cases is 62,924 a day, as of Thursday. While that average is down 14 percent from two weeks earlier, the figure remains near the level of new cases reported during the highest peak last summer. Though fatalities have started falling, in part because of the vaccination campaign at nursing homes, it remains routine for 2,000 deaths to be reported in a single day.

Mr. Biden on Wednesday criticized the decisions by the governors of Texas and Mississippi to lift statewide mask mandates and reopen businesses without restrictions, calling the plans “a big mistake” that reflected “Neanderthal thinking.”

The president, who has asked the American people to wear a mask for his first 100 days in office, said it was critical for public officials to follow the guidance of doctors and public health leaders as the coronavirus vaccination campaign gains momentum.

According to the C.D.C., about 54 million people have already received at least one dose of a Covid-19 vaccine, as of Thursday. Mr. Biden’s power to enforce mask-wearing is limited to the federal sphere; he has ordered a mask requirement for anyone on federal property, and his administration is asking people to wear masks regardless of local mandates.

“It may seem tempting, in the face of all of this progress, to try to rush back to normalcy as if the virus is in the rear view mirror. It’s not,” Andy Slavitt, a White House pandemic adviser, said on Friday. “Why somebody wouldn’t take advantage of a small intervention to save people’s lives, that would be surprising.”

In the latest study, C.D.C. researchers examined the association between mask mandates and indoor or outdoor restaurant dining and the number of coronavirus infections and deaths last year between March 1 and Dec. 31. The agency relied on county-level data from state government websites and measured daily percentage growth in coronavirus cases and deaths.

Infections and deaths declined after counties mandated mask use, the agency found. Daily infections rose about six weeks after counties allowed restaurants to open for dining on the premises, and death rates followed two months later.

Mask mandates were linked to statistically significant decreases in coronavirus cases and death rates within 20 days of implementation, the report’s authors concluded. On-premises dining, whether indoors or outdoors, at restaurants was associated with increases in case and death rates within 41 to 80 days after reopenings.

“State mask mandates and prohibiting on-premises dining at restaurants help limit potential exposure to SARS-Cov-2, reducing community transmission of Covid-19,” the authors wrote.

Shortly after publishing the report, the C.D.C. amended it to urge restaurants that resume on-premises dining to follow the C.D.C.’s guidelines for reducing transmission in restaurant settings.

That includes “everything from having staff stay home when they show signs of Covid or have tested positive or been in contact with someone who has Covid, and requiring masks among employees as well as customers who are not actively eating or drinking,” said Gery P. Guy, a health scientist with the C.D.C. Covid response team and the study’s corresponding author.

Other steps that can be taken are ensuring adequate ventilation, providing options to eat outdoors, spacing customers six feet apart, encouraging frequent hand washing and carrying out frequenting sanitizing of surfaces that are touched a lot, such as cash registers or pay terminals, door handles and tables.

“The message is, if restaurants are going to open for on-premise dining, it’s important to follow C.D.C. guidelines to do so safely and effectively,” Dr. Guy said.

Eileen Sullivan contributed reporting.