Miami (CNN) California Sen. Kamala Harris said Friday that she misinterpreted a question about abolishing private health insurance at Thursday night's 2020 Democratic debate , despite the fact that she raised her hand when asked if she would eliminate it.

NBC's Lester Holt asked for the 10 candidates on stage to raise their hands if their health care plans would "abolish their private health insurance in favor of a government-run plan?"

The California Democrat said she misunderstood the question and believed it was about whether she, personally, would give up her private plan in favor of Medicare.

"So, the question was would you be willing to give up your private insurance," Harris said on "CBS This Morning." When a host pointed out that is not how it was asked, Harris said, "That is certainly what I heard."

"I am supportive of a Medicare for All policy , and under a Medicare for All policy, private insurance would certainly exist for supplemental coverage," she added on CBS.

Harris later told MSNBC that she does not support abolishing private insurance. "No, I do not," she said.

"The question was would you give up your private insurance for that option and I said yes," she noted, continuing with her answer about supplemental care.

Lily Adams, Harris' top communications aide, said on CNN Friday morning that what Harris was saying was "I'm not going to have Medicare for All except for me. She would definitely put herself into a Medicare for All system."

"She's been very clear the bill she supported with Senator Sanders allows for supplemental insurance for those who need it," Adams said. "But, yes, we're going to have to start tackling a real taxing driver of health care costs in this country, which is insurance companies who have continued to drive up premiums, deductibles and copays."

In a statement Friday afternoon, Sanders, while not referring to Harris by name, slammed half measures.

"Let us all be very clear about this. If you support Medicare for All, you have to be willing to end the greed of the health insurance and pharmaceutical industries," Sanders said. "That means boldly transforming our dysfunctional system by ending the use of private health insurance, except to cover non-essential care like cosmetic surgeries. And it means guaranteeing health care to everyone through Medicare with no premiums, no deductibles and no copays."

Harris appeared to tell CNN in January she would eliminate private insurers as a necessary part of implementing Medicare for All

"

The idea is that everyone gets access to medical care, and you don't have to go through the process of going through an insurance company, having them give you approval, going through the paperwork, all of the delay that may require. Who of us has not had that situation, where you've got to wait for approval, and the doctor says, 'Well, I don't know if your insurance company is going to cover this?' Let's eliminate all of that. Let's move on," she said.

Harris aides said that comment was referring to the bureaucracy around health care, but since then the senator has made clear that her vision of Medicare for All "doesn't get rid of supplemental insurance," which she told CNN's Jake Tapper in April.

"No, no, no, no, it does not get rid of insurance," she said. "It doesn't get rid of supplemental insurance."

The question is an important one because it could be a distinction between Sanders, the author of the Medicare for All bill, and Sen. Elizabeth Warren and the host of other Democrats who claim to support some version of it.

"If you want cosmetic surgery — under Medicare for all, we cover all basic health care need — I suppose if you want to make yourself look a little bit more beautiful, work on that nose or your ears, they can do that," he told CBS in April.

And Warren embraced Sanders' vision of Medicare for All during Wednesday night's debate, closing the daylight between the two progressive Democrats atop the 2020 field.

"I'm," she said on Wednesday, "with Bernie on Medicare for All."