“The American people have to be able to trust whoever our party nominates to take on Donald Trump to be straight with them about health care,” Kate Bedingfield, a deputy campaign manager for Mr. Biden, said in a statement late Saturday night. “Senator Warren said tonight that her single-payer plan won’t raise taxes on anyone but billionaires, but that’s simply not true.”

Ms. Bedingfield argued that two other taxes proposed by Ms. Warren would also affect a broader population than just billionaires: a tax on employers that is similar to what they are currently spending on their employees’ health care, and a tax on financial transactions like stock trades.

The issue of Medicare for all has been a major and escalating point of tension between Ms. Warren and Mr. Biden, and a central fault line in the Democratic presidential primary. Mr. Biden supports adding a public health insurance option that people can purchase and building on the Affordable Care Act. He has cast Ms. Warren’s more expansive plan as costly and unrealistic, telling reporters in Des Moines on Saturday that “getting that plan through even a Democratic Congress would be difficult.”

Ms. Warren’s proposal to increase taxes on investment gains did not precisely describe how she would define the top 1 percent of households. In 2017, the top 1 percent of tax returns had income above roughly $515,000, according to the Internal Revenue Service — about 1.4 million tax returns in total. Earlier this year, Forbes said there were 607 billionaires in the United States.

The other measure to tax wealthy Americans that Ms. Warren put forward on Friday would increase her proposed wealth tax on net worth above $1 billion to 6 percent annually, from 3 percent. (Her wealth tax also includes a 2 percent tax on net worth over $50 million, but that remains unchanged from what she proposed in January.)

On Sunday, speaking to reporters in Davenport, Iowa, Ms. Warren offered a broader description of who would face higher taxes under her proposal. “We ask the big corporations and the top 1 percent,” she said, “to pay a little more.”

Matt Flegenheimer contributed reporting from Davenport, Iowa, and Katie Glueck from Des Moines.