WASHINGTON — Senator Elizabeth Warren vowed on Friday to pass major health care legislation in her first 100 days as president, unveiling a new, detailed plan to significantly expand public health insurance coverage as a first step, and promising to pass a “Medicare for all” system by the end of her third year in office that would cover all Americans.

The initial bill she would seek to pass if elected would be a step short of the broader Medicare for all plan she has championed. But it would substantially expand the reach and generosity of public health insurance, creating a government plan that would offer free coverage to all American children and people earning less than double the federal poverty rate, or about $50,000 for a family of four, and that could be purchased by other Americans who want it.

Ms. Warren has long endorsed a Medicare for all bill sponsored by one of her rivals for the Democratic nomination, Senator Bernie Sanders of Vermont. But until now, she has not specified how quickly she would move to enact a health care plan. Friday’s proposal amounts to a detailed road map for eventually establishing Medicare for all, a single government-run health insurance program under which private coverage would be eliminated.

That goal — a wholesale transformation of how Americans receive health insurance — is a big political gamble, particularly given that many of them would have to give up the coverage they get through their employers. Ms. Warren’s proposal for Medicare for all would require an estimated $20.5 trillion in new federal spending over a decade, according to a financing plan she released two weeks ago. To provide funding for it, she would impose new taxes on businesses and the richest Americans.