U.S. schools with mask requirements are seeing fewer outbreaks, the C.D.C. finds.

School mask mandates have generated controversy in many parts of the country. Now, two studies, published on Friday by the Centers for Disease Control and Prevention, provide additional evidence that masks protect children from the coronavirus, even when community rates are high and the contagious Delta variant is circulating.

One study, conducted in Arizona, where children returned to school in July, found that schools that did not require staff and students to wear masks were 3.5 times as likely to have a virus outbreak as schools that required universal masking.

A second study looked at infections among all children in 520 different counties across the United States, and found that once the public school year started, pediatric cases increased at a far higher rate in counties where schools did not require masks.

The first study analyzed data on about 1,000 public schools in Maricopa and Pima counties, which include the metropolitan areas of Phoenix and Tucson, and account for most of the state’s population.

Only 21 percent of the schools implemented a universal mask mandate upon opening, and nearly half had no mask requirement at all. Another roughly 30 percent enacted a mask requirement about 15 days after school started.

Between July 15 and Aug. 31, there were 191 school-associated virus outbreaks that occurred about a week after school started. The majority of them — 113 outbreaks, or nearly 60 percent of the total — occurred in schools with no mask requirement.

Only 16 outbreaks, or 8 percent of the total, took place in schools that implemented mask requirements regardless of vaccination status from the start. There were 62 outbreaks, or about one-third of the total amount, in schools that implemented a mask requirement after the school year had already started.

The study defined an outbreak as two or more positive confirmed cases of infection among staff or students within a 14-day period.

“The school year starts very early in Arizona, in mid-July, so we had the advantage of being able to get an early look at data for the new school year a bit sooner than was possible for the rest of the country, which was important, because of the transmission of the Delta variant,” said J. Mac McCullough, associate professor at Arizona State University and a co-author of the study.

The C.D.C. recommends a layered approach to preventing coronavirus outbreaks in schools — masking, distancing, staying home when sick and vaccination for those eligible. “This study really shines a lens on the masking part of that,” Dr. McCullough said.

The second study looked at the association between school mask policies in a given county and communitywide infections among children, finding that counties with no school mask requirement experienced a larger uptick in pediatric case rates after the start of school than counties with school mask requirements.

Between the week before school started and the second week of school, the number of pediatric infections increased by 35 cases per 100,000 in counties without mask requirements, while the number increased by 16 cases per 100,000 population in counties with school mask requirements.