WASHINGTON — A sweeping new rule issued Tuesday by the Trump administration will make it easier for small businesses to join forces and set up health insurance plans that circumvent many requirements of the Affordable Care Act, cutting costs but also reducing benefits.

President Trump, speaking at a 75th-anniversary celebration of the National Federation of Independent Business, said the new rule would allow small businesses to “escape some of Obamacare’s most burdensome mandates” by creating new entities known as association health plans.

“You’re going to save massive amounts of money and have much better health care,” Mr. Trump said to cheers from the audience of small-business owners. “It’s going to cost you much less.”

As a result, he said, “you’re going to save a fortune.”

Alexander Acosta, the labor secretary, said the rule would give small businesses access to insurance options like those available to large companies, starting as soon as Sept. 1. Millions of people could benefit, he said.