WASHINGTON — President Obama, slipping back into his episodic role as a vigorous campaigner for his new health care act, said Thursday that thanks to the law, more than 8.5 million Americans are getting rebates this summer from their insurance providers.

Mr. Obama was joined by families who have benefited from a provision in the law, which requires health insurers to spend at least 80 percent of the revenue from premiums on medical care rather than on administrative costs. Insurers who fail to meet that benchmark must reimburse customers, a process that began in 2012.

“Last year, millions of Americans opened letters from their insurance companies, but instead of the usual dread that comes with getting a bill, they were pleasantly surprised with a check,” Mr. Obama said in a midday ceremony at the White House.

The checks typically amount to no more than a few hundred dollars. But the president, recounting the stories of middle-class families arrayed on the stage behind him, celebrated these modest windfalls as an early sign of the tangible benefits of the law.