WASHINGTON — More people signed up for Affordable Care Act health plans in the first two days of December than in all of October after the U.S. government rehabilitated its error-prone insurance-exchange website.

About 29,000 people selected health plans through the federal exchange from Dec. 1 through Dec. 2, according to a person familiar with the data who asked not to be identified because the final numbers are being cross-checked. In October about 26,000 people bought health plans through the federal system.

The new numbers provide some hope to the administration that President Obama’s health care overhaul can succeed after the botched Oct. 1 debut of the online insurance marketplaces stymied customers with outages, slow load times and garbled data. Obama on Tuesday began a three-week campaign to regain momentum for his signature initiative.

“We certainly expect enrollment to increase given technical improvements we’ve made to the site,” Joanne Peters, a spokeswoman for the Department of Health and Human Services, said in an email.

The government said Dec. 1 that after six weeks of repairs, it had met goals for making the federal website healthcare.gov, which serves residents in 36 states, fully functional for most users. The 14 states that operate their own exchanges are also reporting improvement.

Peter Lee, the executive director of Covered California has said the state has seen “incredible momentum” since the end of October. Other states, including Washington and Kentucky, also have reported rising interest in enrollment as a Dec. 23 deadline approaches to sign up for coverage that will be effective Jan. 1.

The online exchanges, where people can shop for private health insurance with the help of government subsidies, are at the core of the Patient Protection and Affordable Care Act of 2010. The law requires most Americans to have health insurance by March 31 or pay a fine of as much as 1 percent of income.

Obama has suffered declining approval ratings as problems with the exchange prevented many people from enrolling, even as hundreds of thousands of Americans received letters from their insurers notifying them their current coverage would be canceled at the end of the year.

“I’ve acknowledged more than once that we didn’t roll out parts of this law as well as we should have, but the law’s already working in major ways that benefit millions of Americans right now,” Obama said Wednesday in Washington. “This law is going to work. And for the sake of our economic security, it needs to work.”