SAN FRANCISCO — The University of California’s governing board has adopted a new policy that tightens the rules on affiliations with hospitals that impose religious restrictions on health care.

The new policy follows criticism the UC system has faced for contracts with religious hospitals that refuse to provide services such as abortions, sterilizations or transgender surgery. The UC is fighting legislation by Sen. Scott Wiener, a Democrat from San Francisco, that would require it to end contracts with religious health facilities unless the hospitals changed their policies or did not apply them to UC physicians and students working there.

The vote Wednesday by the UC Board of Regents moved in that direction, but did not require termination of any of the contracts the university says it has with 77 hospitals and other health facilities in California, the San Francisco Chronicle reported. UC officials say the contracts with large chains like Dignity Health, formerly Catholic Healthcare West, allow its medical staff to provide care for 35,000 patients, many of them low-income Californians with little access to hospitals.

“We should have greater ability to serve more patients, but in a way that is in compliance with the policy we adopt today. We’re against discrimination,” said regents Chair John Pérez, author of the resolution the board approved by a 22-0 vote.

The policy allows new contracts only with health care providers that offer their services to all patients, without discrimination, Pérez said.

It would not require a sectarian hospital’s own staff to perform all medical procedures, but it would allow UC personnel at the facilities to do so. And if a patient needed a procedure, such as a hysterectomy or delivery of an ectopic pregnancy, and could not be safely transferred, UC staff would be allowed to perform it at the hospital.

An initial recommended proposal, sent to the regents by UC President Michael Drake’s office, did not create a clear pathway for the UC to phase out hospitals that choose not to comply with the changes.

An amended policy, proposed by Pérez, gives UC-affiliated hospitals with policy-based restrictions until the end of 2023 to comply with the policy, or the affiliation agreement must be canceled.

Drake and Sen. Wiener endorsed Pérez’s amendments.

“It has the potential to significantly expand access to reproductive and gender-affirming care and to ensure UC physicians can exercise their own professional judgment in providing care,” Wiener said in a statement.