Massachusetts hospitals are facing growing financial strains, with more than a third of them losing money last year, according to a new state report.

Two dozen acute care hospitals, 37 percent of the 65 in the state, posted financial losses in fiscal 2011, said the report from the state Division of Health Care Finance and Policy. Among those reporting losses were community hospitals, urban safety net hospitals—which treat large numbers of low-income patients—and even hospitals owned by reowned academic medical centers.

The industry’s health worsened from 2010, when 16 hospitals posted losses, and 2009, when 13 were unprofitable.

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Overall, profit margins for the state’s 65 acute care hospitals fell to 2.1 percent in 2011 compared with 2.6 percent during the prior year, the report said. It depicts a health care market that was scrambling to adjust to rapid changes even before the Massachusetts legislature passed a law this summer designed to rein in soaring medical costs.

Some of the deepest losses were registered by big safety-net institutions such as Boston Medical Center and Cambridge Health Alliance, which are heavily dependent on government insurance programs that pay for the care of low-income patients.

But three hospitals owned by the giant Partners HealthCare System, including Faulkner Hospital in Jamaica Plain and North Shore Medical Center in Salem, also lost money, as did eight owned by Steward Health Care System—among them, St. Elizabeth’s Medical Center in Brighton and Carney Hospital in Dorchester. Also on the list are Beth Israel Deaconess Medical Center- Needham and Boston’s Dana-Farber Cancer Institute.