WASHINGTON — More than 1.1 million people signed up for health insurance through federal and state marketplaces in January, according to the government, and the number of young people enrolling increased faster than that of any other group.

The results were hailed by Obama administration officials, who expressed increased optimism that they had overcome their initial stumbles and erased many doubts about the viability of the health care law.

Most promising, according to the Department of Health and Human Services, is that 25 percent of those signing up for insurance from October through January were ages 18 to 34 — the young and presumably healthy people whom insurance companies need as customers in order to keep premiums reasonable for everyone.

“These encouraging trends show that more Americans are enrolling every day, and finding quality, affordable coverage in the marketplace,” said Kathleen Sebelius, the secretary of health and human services.