WASHINGTON — Enrollment through insurance marketplaces created by President Obama’s health law rose sharply in November, as more than 250,000 people selected health plans in the month, according to a new government report.

That was more than double the number who signed up in October, when problems with the new HealthCare.gov website made enrollment virtually impossible for long stretches of time.

The increasing numbers of Americans signing up for health coverage are fueling renewed optimism among supporters of the Affordable Care Act, who hope that fixes to the federal site could rescue the law, known as Obamacare, from its disastrous debut.

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“We think we are on track and we will reach the total that we thought,” said Michael Hash, director of the Office of Health Reform at the Department of Health and Human Services, which produced the report.

The report also outlines very strong consumer interest in health insurance, with 3.7 million people nationally submitting applications in October and November for health insurance through state and federal marketplaces.

Of those, more than 803,000 were deemed eligible for government Medicaid and Children’s Health Insurance Program coverage.

The health law created the marketplaces for Americans who do not get health coverage at work.

Consumers can go to a market and select among health plans that must offer a basic set of benefits. Consumers making less than four times the federal poverty level – or about $94,000 for a family of four – qualify for government subsidies to offset the cost of their premiums.

In half the states, very poor Americans will qualify for virtually free Medicaid coverage under the law.

The November enrollment tally still leaves the Obama administration far below its target of enrolling 7 million people in health plans sold through the new marketplaces.

And the administration has not even come close to balancing the millions of people who have lost health coverage because their insurance companies canceled health plans that do not meet new standards outlined by the health law.

It also remains unclear how many of the people who signed up for health coverage will actually get an insurance card.

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Widespread problems in the transmission of consumer information from HealthCare.gov to insurance carriers prompted the Obama administration to estimate that as many as a quarter of the application processed in October and November contained errors.

Julie Bataille, a spokeswoman for the agency running HealthCare.gov, said Tuesday that federal officials continue to work with insurers to correct those errors, but she would not say how many of the applications had been verified.

Even with the ongoing problems, the latest enrollment report marks a major improvement on October’s tally, when a paltry 106,000 people nationwide selected a marketplace health plan.

The acceleration in sign-ups was particularly pronounced in the 36 states that rely on the federal government and its HealthCare.gov site for enrollment.

More than 110,000 chose a plan in November through a federally run marketplace, more than four times the number in October.

Enrollment on the federal marketplaces increased even more quickly in the first week of December after major website repairs were made, with more than 50,000 additional sign-ups, according to an official knowledgeable of the numbers. December enrollment numbers have not yet been officially tallied.