“But it doesn’t cost $3 trillion, and it can be done quickly,” he continued, when asked about differences among the Democratic candidates. “I don’t know why we’d get rid of what in fact is working and move to something totally new. And so, there are differences.”

A day earlier, as he navigated a dripping ice cream cone while speaking to reporters in Portsmouth, Mr. Biden echoed President Barack Obama as he said that his vision would “allow people who in fact like their private insurance, or like their employer-based insurance, to be able to keep it.” And he also mentioned one of his opponents by name.

“Bernie’s been very honest about it,” he said, of Medicare for All. “He’s said you’re going to have to raise taxes on the middle class. He says it’s going to end all private insurance. I mean, he’s been straightforward about it and he’s making his case.”

Asked if other contenders have been equally direct about Medicare for All’s costs, he replied, “So far, not. So far, not. They may. They may.”

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In an interview, Mr. Sanders, who introduced the Medicare for All Act in the Senate and sometimes comes in second to Mr. Biden in early polls, bristled at Mr. Biden’s remarks, as he stressed that he, too, had been committed to passing and protecting the Affordable Care Act, even as he now advocates for something more far-reaching.

He also took issue with what he perceived as Mr. Biden’s suggestion that the transition to Medicare for All could leave people with gaps in medical care, calling such an implication “totally absurd.”