WASHINGTON — The Obama administration said on Monday that 16.4 million uninsured people had gained health coverage since major provisions of the Affordable Care Act began to take effect in 2010, driving the largest reduction in the number of uninsured in about 40 years.

Since the first open enrollment period began in October 2013, the officials said, the proportion of adults lacking insurance has dropped to 13.2 percent, from 20.3 percent.

Sylvia Mathews Burwell, the secretary of health and human services, said the data revealed “the largest reduction in the uninsured in four decades.” Many people gained coverage after the creation of Medicare and Medicaid in 1965.

White House officials said the figures disproved the charges leveled by some Republicans opposed to the law, including governors who have declined to expand their Medicaid programs.