The top health official who created the San Francisco program, Mitchell H. Katz, is now the head of New York City’s hospital system and will oversee the city’s effort, branded as NYC Care. “It’s a much bigger and more compassionate vision,” said Mr. Katz, comparing New York’s proposed program to the much smaller one in San Francisco.

The mayor was quick to say that the plan would not be a substitute for any universal health care at the state level or a national single-payer plan. But, aides said, it was something the city could do immediately and on its own, without approval from the State Legislature, which is weighing some form of universal health insurance for New York State.

Indeed, the mayor’s proposal is a mix of insurance and direct spending, and Mr. de Blasio said it would take about two years to get it fully running. The city already has a kind of public option for health insurance for low-income New Yorkers, through an insurance plan run by city hospitals known as MetroPlus.

The new proposal would improve that coverage, which already insures some 516,000 people, and aim to reach more of those who are eligible, such as the young and uninsured, and others who qualify but have not applied.

It would also provide additional direct city spending, at least $100 million per year when fully implemented, officials said, for the city’s hospital system to support care for those without insurance. The city estimates the uninsured population to be about 600,000 people, including as many as 300,000 undocumented residents. A major component of that effort would be improving customer service, including the phone line, to help those with questions about their care.

Part of the goal of NYC Care, aides to the mayor said, was to direct people to medical care earlier — before they seek more expensive services in an emergency room — while providing them with better health care.

The effort is also aimed at getting some of the so-called young-and-invincible uninsured population into the health care system, either through the city’s insurance plan or through its hospital system.