WASHINGTON — Midway through sign-up season, more young adults are getting coverage through President Obama’s health care law. The number of new customers is also trending higher, officials said Tuesday in an upbeat report.

Outside analysts who reviewed the administration’s update said it reflects encouraging progress, but that may not dispel questions about the long-term future of the health insurance markets created under Obama’s 2010 overhaul. Premiums have been going up and getting new sign-ups remains a challenge.

Administration statistics also showed some continuing problems verifying the citizenship and income of applicants for subsidized coverage. Consumer advocates say those issues generally stem from the complexity of the law, and that many people who run into verification problems simply drop out. Some become uninsured again.

Health and Human Services Secretary Sylvia M. Burwell said more than 8.2 million people signed up or renewed coverage for 2016 from Nov. 1 through Dec. 19. Open enrollment ends on Jan. 31. People who remain uninsured after that risk rising fines.

“We’re off to a strong start,” Burwell said Tuesday, noting that the numbers reflect only the 38 states using the HealthCare.gov website and call center. Major states running their own programs, including California and New York, were not counted in Tuesday’s report, and their totals will be factored in later.

About 2.4 million people who’ve signed up are new to HealthCare.gov, said Burwell, ahead of last year’s levels. And 2.1 million are under age 35, a coveted demographic because young adults tend to be healthy and their participation helps keep premiums in check. The number of younger adults signed up is close to double what it was at this point last year.