After years of growing concern about obesity among children, federal researchers have found the clearest evidence yet that the epidemic may be turning a corner in young children from low-income families.

The obesity rate among preschool-age children from poor families fell in 19 states and United States territories between 2008 and 2011, federal health officials said Tuesday — the first time a major government report has shown a consistent pattern of decline for low-income children after decades of rising rates.

Children from poor families have had some of the nation’s highest rates of obesity. One in eight preschoolers in the United States is obese. Among low-income children, it is one in seven. The rate is much higher for blacks (one in five) and for Hispanics (one in six).

Several cities have reported modest drops among school-age children, offering hints of a change in course. But gains were concentrated among whites and children from middle- and upper-income families, and were not consistent across the country.