WASHINGTON — More than 16 million Americans have gained coverage since President Barack Obama’s health care law took effect five years ago, the administration said Monday. But an independent expert who used some of the same underlying data had the much lower estimate of 9.7 million.

The Department of Health and Human Services estimated that 16.4 million adults have gained health insurance since the law’s major coverage provisions began taking effect in 2010. At the same time, data from a large daily survey called the Gallup-Healthways Well-Being Index show that there are 9.7 million fewer uninsured adults now compared with the first part of 2010.

There seems to be no dispute that the law has significantly reduced the number of uninsured Americans. The question is, by how much?

The HHS estimate comes as the administration prepares to commemorate the fifth anniversary of the law’s signing on March 23, 2010. The Affordable Care Act has been politically divisive from the start.

Democrats hailed the law’s passage as the culmination of decades of effort to guarantee health coverage for all Americans, including people with health problems who previously could be turned away by insurance companies.

Republicans called it government overreach, and haven’t stopped trying to repeal or roll back what they dismiss as “ObamaCare.” That opposition has helped the GOP win control of Congress.

The health care law offers subsidized private coverage for people who don’t have health insurance on the job, along with an expanded Medicaid program that a majority of states have accepted.