Of insurance companies, he said, “Their job is to take in as much money as they can and pay out as little as they can.” The complexity and delays of private insurance processing are no accident, he added: “They make money on the float.”

Depending on the recommendations of a government task force he would create under a deputy mayor of health care innovation, he said, city coverage might still be placed in the hands of a different insurance company under a more competitive scheme, or the city might outsource just the administration to an insurer, as Medicare does while keeping overhead as low as 1.3 percent. A third option he listed would be for the city “to take the whole thing in-house.”

He said he would reorganize government agencies to seize opportunities presented by the Affordable Care Act, and have his health care innovation task force consider insurance terms that “keep more of the money in the city,” like allowing prescriptions to be filled at local pharmacies rather than only by mail order, or using the city’s development and investment capability to increase primary care at a hospital facing closure.

“This is not just a conversation you can have around cost,” he said, citing the nation’s experience in the 1990s with an H.M.O. model that no one liked, and calling the quality of health care in New York “a crown jewel.”

The coverage devised by the task force, which he called Thrive (standing for Taskforce for Healthcare Reform, Innovation and Vitality for Everyone), could eventually be offered to all New Yorkers by being listed on the state insurance exchange required by the Affordable Care Act. Such an experiment could not be tried in places like Cincinnati or St. Paul, he went on, but “New York is the health care capital of the world,” with more than 560,000 health care workers, including tens of thousands of doctors and nurses in the city’s own employ.