The data may bolster Democrats’ claims that the law is working as they intended, but it is unlikely to prompt Republicans to let up on criticism of the law, which was passed without any Republican votes.
In a report on its findings, the center said that the proportion of the population without insurance had declined by five percentage points, to 9.2 percent, in the first quarter of this year, from 14.4 percent in 2013.
Among people age 18 to 64, the number who were uninsured dropped by about one-third, to 25.5 million, in the first quarter of this year, from 39.6 million in 2013. And among children under 18, the number of uninsured declined to 3.4 million this year, from 4.8 million in 2013.
The decline in the number of uninsured coincides with improvements in the economy. In the last two years, the recovery has gained traction and the unemployment rate has declined steadily.
The numbers for the first quarter of this year, from the National Health Interview Survey, are estimates based on data for 26,121 people. The information was collected in household interviews by the Census Bureau, using procedures specified by the National Center for Health Statistics, a part of the Public Health Service. The survey focused on the civilian population outside prisons and nursing homes.
The report suggests that the Affordable Care Act produced the most significant gains in coverage among poor people and those with income just over the poverty level, which is $11,770 for an individual.
In the first three months of this year, among poor people age 18 to 64, about 28 percent lacked health insurance, down from 39.3 percent in 2013, the government said. And among people in that age bracket with incomes from the poverty level up to twice that amount, 23.8 percent were uninsured in the first quarter of this year, down from 38.5 percent in 2013.
Gains in coverage were also notable for Hispanics, who have long been more likely than other groups to be uninsured. In the first quarter of this year, 28.3 percent of Hispanics age 18 to 64 were uninsured, down from 40.6 percent in 2013, the government said.
The comparable figures also fell for non-Hispanic black adults, to 15.6 percent from 24.9 percent, and for non-Hispanic white adults, to 8.7 percent from 14.5 percent.
States that expanded Medicaid have seen a sharper drop in the proportion of people who are uninsured, although residents of those states were also more likely to have coverage before the health law took effect. In states that expanded Medicaid, 10.6 percent of people age 18 to 64 were uninsured in the first quarter of this year, down from 18.4 percent in 2013, the report said.
In states that chose not to expand Medicaid, 16.8 percent of such adults were uninsured in the first quarter of this year, down from 22.7 percent in 2013.
A separate study, issued this week by the Gallup organization, found that Texas was the only state where at least 20 percent of people were uninsured. By contrast, it said, in 2013, people without coverage accounted for at least 20 percent of the population in 14 states. Arkansas, California and Kentucky were among the states showing the largest reductions in the proportion of people without insurance.
The data, collected in telephone interviews as part of the Gallup-Healthways Well-Being Index, showed that the uninsured now account for 5 percent of the population or less in seven states: Connecticut, Hawaii, Iowa, Massachusetts, Minnesota, Rhode Island and Vermont.
From 2008 to 2014, Massachusetts was the only state at or below 5 percent, Gallup said. Massachusetts expanded coverage under a 2006 law that was, in some ways, a model for the federal law signed four years later by President Obama.
Correction: August 13, 2015
A chart on Wednesday with an article about a decline in the number of Americans without health insurance transposed, in some editions, labels showing the uninsured rates for adults considered near-poor or poor. The rate for poor adults is higher, at 28 percent, and the rate for near-poor adults is lower, at 23.8 percent. In addition, the share of adults considered not poor who were uninsured was 7.5 percent, not 4.6 percent. A corrected chart can be found at nytimes.com/us.