Mr. Bloomberg’s plan would also ban surprise medical bills from out-of-network providers who see patients at in-network hospitals. Congress came close to passing such a measure this year but left the policy out of a year-end spending package after lawmakers became reluctant to pass a measure that would cut doctor pay.

The Bloomberg campaign estimated that, in total, his health plan would require an additional $1 trillion in tax revenue over the next decade. A senior policy adviser cautioned that the figure was preliminary and “loosey-goosey,” saying the campaign would follow up with a more robust financial analysis.

Mr. Bloomberg is the second candidate to roll out a health care platform this week, in a campaign cycle where the issue remains top of mind for voters. The entrepreneur Andrew Yang on Monday released a set of more incremental changes to the health system. He described himself as supporting “the spirit of Medicare for all” but did not propose a new government health plan. Instead, he suggested policies such as discouraging malpractice suits and expanding mental health coverage.

Mr. Bloomberg’s support for a public option in health care stretches back a decade to when he was mayor. He urged Congress to adopt such a policy in 2009, when Democrats were debating the law that would become the Affordable Care Act.

“I support the concept of a public plan, because if it’s done right, it means introducing exactly the kind of competition our system needs,” Mr. Bloomberg wrote in an op-ed published in The New York Daily News in 2009.

The public option ultimately fell out of the Democrats’ health plan after facing intense opposition from the health insurance industry and failing to get enough support from lawmakers.

Some candidates, such as Ms. Warren, envision the public option as a steppingstone on the path to a Medicare for all system. She has proposed passing a public option in the first 100 days of her presidency and expanding that into government coverage for all Americans by the end of her third year.