WASHINGTON—President Barack Obama, reviewing his signature health law six years into its implementation, is suggesting Congress and his White House successor add a government-run, or public, insurance option to the Affordable Care Act and increase federal financial assistance for people to buy coverage.

Writing as Barack Obama, J.D., in the Journal of the American Medical Association, the president lauded the health-care overhaul and excoriated its opponents, arguing the law has sharply reduced the number of uninsured in the...