Public hospitals in the United States are being overwhelmed by a rising tide of uninsured poor, low-income AIDS patients and victims of shootings and urban violence, hospital officials said yesterday. They asked for up to $2 billion annually in federal funds to avoid severe erosion or even collapse.

Larry Gage, president of the National Association of Public Hospitals, released a study finding that despite assistance from state and local governments, large public hospitals had an average operating loss of $9.4 million in 1988, leaving no margin for emergencies, renovations and sudden upsurges in patient-care costs.

"The situation of most has continued to deteriorate since the 1980s," Gage said. He said the cause was the general increase in health-care costs, the failure of Medicaid and Medicare in many cases to reimburse hospitals fully for the costs of patient care and the fact that more than 30 million people who have no insurance come to public hospitals for free care.

Mark Chastang, general executive director of D.C. General, said that as the only public hospital in the District it has responsibility to care for people who cannot get care elsewhere. He said the hospital had a $7 million net deficit in fiscal 1989. The number of uninsured has grown "dramatically" in recent years, Chastang said, and they currently make up 58 percent of the total patient load. The financial shortfalls have forced many public hospitals to cut back on services, Chastang said.

Gage said public hospitals exist to guarantee that there is a basic core of services available in their communities. These include emergency room services, burn centers and trauma centers, free care for the poor, AIDS care, neonatal intensive care and many other specialty services. The survey covered 57 major large public hospitals in large cities.

Gage said the survey found that the loss on caring for the indigent and those with inadequate insurance averaged $40.7 million in 1988 at the 57 hospitals. That was one-quarter of all uncompensated care by the nation's 6,000 hospitals. General subsidies from the state or local government and profit margins on the care of paying patients offset part of this, but the average operating loss was still $9.4 million.

The association's figures show that at D.C. General total revenue in 1988 was $110.4 million, about $42 million of which came from the District government. The hospital also received D.C. Medicaid payments. At New York's Bellevue, $44 million of the hospital's $289 million total revenue was a city or state subsidy.

The figures show that the public hospitals had high bed-occupancy rates, exceeding 80 percent, but many of these patients were nonpaying. About one-third of all inpatient days and half of all emergency room and outpatient visits in hospitals covered by the survey were for patients with no health insurance or other source of payment.