In the health law’s first year, the number of uninsured patients the system treated dropped by only 1.3 percent, the report said; another decrease of 7.2 percent is projected by 2019.

Image Comptroller Scott M. Stringer released a report on Monday calling on the federal government to delay the cuts until their impact can be better assessed. Credit... Fred R. Conrad/The New York Times

More strikingly, the city’s hospital system has not attracted enough newly insured patients to give it the revenue increase it would need to make up for the loss of federal funds, the report says.

“We have a solemn commitment to fund H.H.C. so that it can serve everyone who walks through the door, regardless of their immigration status or ability to pay,” Mr. Stringer said in a statement, referring to the Health and Hospitals Corporation, which runs the public hospitals. “That’s why we need to find a real cure for these cuts, not just apply a Band-Aid.”

The 11-hospital system expects to face a deficit of more than $1 billion in fiscal year 2017, which will grow in subsequent years, the report said. The city’s taxpayers are ultimately responsible for filling that gap.

The report projects that the system’s cash on hand, an indicator of financial stability, will drop to $44 million, from $1 billion, by 2019-2020, largely because of the projected $827 million loss in federal “disproportionate share” subsidies.