SAN FRANCISCO — The Board of Supervisors upheld San Francisco’s status as a sanctuary for immigrants on Tuesday, unanimously passing a resolution that called on local law enforcement not to notify the federal authorities when unauthorized immigrants are released from custody.

The city had been under pressure from critics of its policies on immigrants after Kathryn Steinle, 32, a tourist from Pleasanton, Calif., was fatally shot in the chest in July while walking with her father along the Embarcadero waterfront. The man accused of the shooting, Juan Francisco Lopez-Sanchez, is an unauthorized immigrant who has been deported to Mexico five times for various felonies, including drug charges, and had been released from a San Francisco jail shortly before the killing.

At the same time, the board put off a vote on a hotly debated resolution that would have asked the San Francisco sheriff, Ross Mirkarimi, to rescind a March memo instructing staff members not to give information about detainees, such as immigration status, arrest records and release dates, to federal immigration officials.

Policies regarding sanctuary cities vary, but San Francisco has generally protected unauthorized immigrants without criminal records from deportation agents.