WASHINGTON — Approximately 11.4 million people have signed up for health coverage through the Affordable Care Act this year, President Barack Obama announced Tuesday, signaling a strong conclusion to the federal health law’s second enrollment period.

With thousands more people expected to enroll in the coming days as applications for coverage are completed and processed, the total will likely increase.

That should ensure that the final 2015 tally will easily exceed last year’s enrollment total and mark further progress in the law’s program for expanding coverage.

More still may enroll if the Obama administration decides to hold a special enrollment period after April 15. The administration has been considering doing so to allow people who had to pay a penalty for not having health coverage in 2014 get insurance this year and avoid a second year of penalties.

“It gives you some sense of how hungry people were out there for affordable, accessible health insurance,” Obama said in a two-minute video posted on Facebook that features him speaking in the Oval Office with Health and Human Services Secretary Sylvia M. Burwell over a background soundtrack.

“The Affordable Care Act is working,” Obama said in the video.

The 2010 law allows Americans who don’t get health benefits at work to shop among private insurance plans sold on state-based marketplaces operated by the federal government or by the states.

Consumers making less than four times the federal poverty level — or about $94,000 for a family of four — qualify for subsidies. Insurers must provide a basic set of benefits and cannot turn away consumers, even if they are sick.

About 6.5 million people had health coverage through the marketplaces at the end of 2014 — a lower total than the 8 million who initially signed up, as some people dropped their plans or switched to other coverage through the year.

This year, the administration sought to lower expectations, saying about 10 million would enroll.