Former Mayor Michael R. Bloomberg of New York unveiled a health policy proposal on Thursday that would create a government-run health insurance plan but not provide universal guaranteed coverage, aligning himself with the more moderate wing of the Democratic Party in the 2020 presidential primary.

The plan, which he was set to announce at a campaign event in Tennessee, is among Mr. Bloomberg’s first policy rollouts. It echoes similar plans released by some rivals, including former Vice President Joseph R. Biden Jr. and Mayor Pete Buttigieg, which give Americans the option of buying public insurance but stop short of moving the entire country to a “Medicare for all” system advocated by progressives like Senators Bernie Sanders and Elizabeth Warren.

In a primary that has featured a fierce battle over how much a Democratic president ought to disrupt the health care system, Mr. Bloomberg’s plan places him firmly in the camp that believes smaller changes can make medical care more affordable while preserving the private insurance more than 150 million Americans receive through their employers.

Proponents of Medicare for all, by contrast, say the government should provide health coverage for everyone and want to eliminate most private insurance plans.

In staking out his position, Mr. Bloomberg is wading into a debate that has drawn the four leading candidates into heated exchanges. Mr. Biden and Mr. Buttigieg have warned that Medicare for all would force Americans to give up their existing health coverage, and have questioned how a universal government plan would be paid for. Mr. Sanders and Ms. Warren have said their rivals’ plans would maintain an unfair private insurance system.

Mr. Bloomberg instead focuses on building on the policies in the Affordable Care Act, a law that has faced consistent threats of repeal since its passage in 2010. The most recent effort is a lawsuit led by Republican attorneys general arguing that the health law is unconstitutional. A federal appeals court on Wednesday struck down the law’s mandate to purchase coverage, but sent questions about the rest of the law’s viability back to a district court.