Nearly 80,000 people have enrolled in health plans through California’s online marketplace, at a rate of several thousand a day in November — a sizable increase over a month ago, state officials said on Thursday.

Especially encouraging, officials said, was the enrollment of young people, who are considered essential to the success of the Obama administration’shealth care law.

Shortly after the numbers were released, the board of Covered California, the state exchange, voted against going along with a proposal by President Obama to consider renewing previously canceled plans, saying the move would undermine the state marketplace’s growing success.

California joins at least seven other states that have declined to go along with the proposal, which Mr. Obama made after a wave of cancellations across the country created a furor and led to complaints that he had reneged on his promise to let consumers keep plans they liked.

“Delaying the transition is not going to solve a single problem, it just pushes the problem down the road,” Susan Kennedy, a member of the five-person board, said just before the vote. “I actually think it’s going to make a bad situation worse by complicating it further.”

The state’s enrollment figures represent a rare bright spot in the unfolding story of the Affordable Care Act. Its rollout has been troubled by technical problems with the federal health care website, lower-than-expected enrollment and a public outcry over its role in the cancellation of millions of insurance plans.

Officials said 18- to 34-year-olds made up 22.5 percent of the nearly 31,000 Californians who selected a private health plan in October. The same age group makes up 21 percent of the state’s population.

The enrollment of young people is important to insurers because their relative good health offsets the costs for people with serious medical conditions.

“Enrollment in key demographics like the so-called young invincibles is very encouraging,” Peter V. Lee, the executive director of Covered California, said in a statement.

Young Invincibles, a health care advocacy group for young people, said in a statement that the news out of California shows “that young adults are engaged and excited about their new options even at this very early stage in the enrollment process.” It noted that California was a crucial state for recruiting young people because 31 percent of those living there lacked health insurance.

Officials said that over 10,000 applications for coverage were now being completed each day, with more than 360,000 applications having been completed through Tuesday. Those numbers include people who are also eligible for Medi-Cal, California’s no-cost health insurance program for the poor.

Like many of the 16 states and the District of Columbia that are operating their own marketplaces, California’s health insurance website has run far more smoothly than the federal website, which handles the online enrollment for 34 states that declined to set up their own exchanges. In November, roughly 2,700 people were enrolling each day, California officials said. That is up from 700 people a day when the site opened last month.

The federal site has been plagued by technical problems since it opened on Oct. 1. In contrast to California, only about 27,000 people enrolled in private plans through the federal website in October, although enrollment reportedly picked up in the first half of November.

People who did not qualify for a subsidy enrolled in significantly higher numbers than those who did. The state reported that 4,852 people who selected a private plan in October were eligible for tax credit subsidies, which are based on income, compared with 25,978 who did not qualify.

Timothy S. Jost, a health care expert at Washington and Lee University, said the same pattern emerged in the federal marketplace statistics released for October. “I suspect this is reasonably well-off people who are losing coverage in the individual market and have found good coverage on the exchange,” he said.

That may be one reason for the California board’s decision against allowing people to renew plans that had been canceled in the state. California had required all carriers that were participating in the exchange to cancel any existing plans that did not comply with the new law by Jan. 1.

The state’s insurance commissioner, Dave Jones, lambasted the Covered California board’s decision as a “disservice to California’s consumers.”

Mr. Jones took issue with the board’s reasoning, saying, “Allowing them to renew as the president has called for will not harm the exchange or the implementation of the Affordable Care Act in California, nor will it harm the individual market risk pool.”

Several of the other states that most enthusiastically supported the new health care law, including Massachusetts and New York, have also resisted the president’s proposal, also contending that the move could jeopardize their fledgling state insurance marketplaces.