WASHINGTON—Some 11.4 million Americans picked health plans through HealthCare.gov and state-run insurance exchanges during the official sign-up window for insurance under the federal health law, the White House said Tuesday.

The announcement, made through the White House Twitter account, followed a relatively smooth enrollment period that saw few of the technological problems that hobbled the online exchanges that were launched in the fall of 2013 as part of the Affordable Care Act.

The White House posted a video of Sylvia Mathews Burwell, secretary of the Department of Health and Human Services, giving the news to President Barack Obama in the Oval Office. “That’s great,” Mr. Obama replied.

“It gives you some sense of how hungry people were out there for affordable, accessible health insurance,” Mr. Obama said later in the video. “The Affordable Care Act is working. It’s working a little better than we anticipated. It’s certainly, I think, working a lot better than many of the critics talked about early on.”

The Obama administration has said around 6.7 million people were enrolled in health plans ahead of the new sign-up window. The administration closed out the last sign-up period, which lasted six months, with around 8 million people who had picked plans through the exchanges.

The latest sign-up number includes millions of people who bought coverage in 2014 and were automatically re-enrolled in coverage for 2015, as well as people who came back to the sites to pick new plans, people who had previously been uninsured, and people who had had other coverage but lost it for 2015.

It likely doesn’t include all of the people who were trying to get coverage on HealthCare.gov, which serves 37 states, or on one of the 13 state-run sites when the sign-up deadline passed at 11:59 p.m. Pacific time Sunday. The federal government said Monday that it would give those people through Feb. 22 to finish applying for coverage and picking their plans, and most states have followed suit. Ms. Burwell said in her filmed conversation with the president that the numbers were “preliminary.”

The tally puts the Obama administration on track to meet its goal of having between nine million and 10 million people enrolled in individual coverage through the exchanges by the end of 2015.

Some people who have picked plans through the sites are unlikely to pay their first month’s premium, the final step needed for insurance coverage. Others are expected to drop their health plans over the course of the year, because they get insurance through a job or government program such as Medicare, or because they no longer want it.

But that target, announced by Ms. Burwell shortly before the enrollment window opened on Nov. 15, was lower than some earlier estimates for 2015. The nonpartisan Congressional Budget Office had projected that 13 million people would use the exchanges in 2015, and it has subsequently put the number at 12 million.

Obama administration officials have said they are considering extending the sign-up period through the end of tax-filing season because many people are expected to learn they must pay a tax penalty for going uninsured.

On Monday, Washington state became the first to extend the sign-up deadline until mid-April, allowing uninsured people to get health plans on the state-run exchange while filing their tax returns.

Write to Louise Radnofsky at louise.radnofsky@wsj.com

Source – Wall Street Journal