A day after Senator Kamala Harris of California endorsed ending private health insurance in favor of a “Medicare for all” government plan, Michael R. Bloomberg, a possible rival of hers for the Democratic presidential nomination, said the proposal would “bankrupt us for a very long time.”

Mr. Bloomberg, the former New York City mayor who is considering a 2020 bid on a centrist Democratic platform, rejected the idea of “Medicare for all,” which has been gaining traction among Democrats.

“I think you could never afford that. You’re talking about trillions of dollars,” Mr. Bloomberg said during a political swing in New Hampshire, which holds the nation’s first primary in 2020.

“I think you can have ‘Medicare for all’ for people that are uncovered,” he added, “but to replace the entire private system where companies provide health care for their employees would bankrupt us for a very long time.”