Sen. Kamala Harris said Friday that she does not support eliminating private health insurance, after she and Sen. Bernie Sanders raised their hands in response to a question from debate moderators about whether they would abolish private health insurance in favor of a government-run plan at the Democratic debate Thursday.

Harris told "CBS This Morning" on Friday that she had misheard the question by debate moderator Lester Holt.

Holt had posed the question, "Many people watching at home have health insurance through their employer. Who here would abolish their private health insurance in favor of a government-run plan?"

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Harris and Sanders were the only two to raise their hands.

The California Democrat said that she had interpreted the question to mean, "Would you be willing to give up your private insurance?" She said that her answer was for herself personally, but that she believed private insurance could still supplement "Medicare for All."

"I am supportive of Medicare for All. And under Medicare for All policy, private insurance certainly exist for supplemental coverage," Harris told "CBS This Morning." "But under Medicare for All, in my vision of it, we would actually extend benefits."

Of the 20 candidates who appeared at the debate this week, only Sanders and Sen. Elizabeth Warren support fully abolishing private health insurance.