Still, most teenagers were falling short of federal recommendations, which call for children to get at least an hour of physical activity daily, a central message of Michelle Obama’s signature “Let’s Move” campaign. The new data showed that most children engaged in an hour of exercise fewer than five days a week and spent more than two hours a day watching television, chatting online and playing video games.

The numbers also revealed something of an age and racial divide. Younger children had the highest levels of physical activity and fruit and vegetable consumption. But as children got older, the frequency of eating junk foods and engaging in sedentary behaviors crept up, along with average body mass index, a crude measure of obesity.

Black and Hispanic adolescents lagged behind whites on almost every measure of progress, even after the researchers tried to take into account the influence of socioeconomic factors.

“In some ways you can interpret what we found positively by saying we’re beginning to bend the curve, and hopefully we’ll start seeing a downward trend in obesity,” said Dr. Ronald J. Iannotti, a study author and chair of the department of exercise and health sciences at the University of Massachusetts Boston. “But there’s large room for improvement.”

The study analyzed data from a national survey of tens of thousands of schoolchildren in grades 6 through 10, which was carried out once every four years from roughly 2001 to 2010.

Childhood obesity rates, which have more than doubled since 1980, rose slightly between 2001 and 2006, then leveled off by 2010, at roughly 13 percent. The proportion of those who were overweight also plateaued at around 17 percent.

Obesity tends to follow children into adulthood, raising the risk of heart disease and cancer as well as Type 2 diabetes, a disease that has also risen sharply among children.

In the past year, other studies have hinted at improvements in the obesity rate among younger children, with some even showing a decline in some cities. But little was known about the extent to which physical and dietary behaviors might have played a role.

The new study found that at the same time obesity and overweight appeared to level off, there were, on average, very slight increases in physical activity, fruit and vegetable consumption and the eating of breakfast, another habit public health officials consider a marker of healthy behavior.

The opposite trend was seen for behaviors that are widely discouraged. The amount of time teenagers spent watching television fell from about three hours a day in 2001 to less than two-and-a-half hours by 2010. Teenagers also reported drinking slightly fewer soft drinks and eating less candy.

Boys overall reported more physical activity than girls, but they also watched more television and played more video games and ate fewer fruits and vegetables.

One expert who was not involved in the study, David B. Allison, the director of the Nutrition Obesity Research Center at the University of Alabama at Birmingham, said it was impossible from the data to deduce a cause and effect, since any number of factors that could influence obesity rates may have changed over time.

“We should be very cautious about drawing any attributions about causes based on time trend data,” Dr. Allison said.

But Dr. Iannotti said the findings seemed to suggest a pattern. “I think the public health message is beginning to be accepted,” he said.

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