Senator Kamala Harris of California, who is increasingly seeking to carve out an ideological lane separate from the most progressive Democrats running for president, laid out a new plan Monday for providing Medicare for all Americans, with a twist that stops short of the complete overhaul of the health insurance system that Senator Bernie Sanders of Vermont has proposed.

Ms. Harris’s announcement comes as the Democratic candidates are preparing for a fresh round of debates this week, and as she faces mounting pressure to clarify her stance on the issue after repeated missteps. It also comes as fellow candidates, such as Mr. Sanders and former Vice President Joseph R. Biden Jr., have sparred over health care in recent weeks.

The issue has become a litmus test among the 2020 Democrats, separating the candidates of the progressive left, who want to move rapidly toward a single-payer health care system, and the more moderate contenders, who favor other ways of expanding coverage and lowering costs.

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Ms. Harris’s proposal seeks to straddle both camps, using the “Medicare for all” mantra as a long-term target while also seeking to keep a significant role for private insurers — which Mr. Sanders’s plan would eliminate.