San Francisco supervisors will try Tuesday to decide whether to continue a policy that prevents cooperation with federal immigration officials that gained attention when a man in the country illegally killed a woman on a city pier.

The Board of Supervisors will consider two non-binding but strongly symbolic resolutions nearly four months after 32-year-old Kate Steinle was shot by a Mexican national who had been released from jail despite federal requests to detain him for deportation proceedings.

One resolution would reaffirm the so-called sanctuary policy, while the other would soften it by allowing sheriff's officials to talk with federal authorities about prisoners that could be subject to deportation.

The death of Steinle cast an uncomfortable spotlight on the city that proudly declares itself a refuge for immigrants. As outrage mounted nationally, U.S. Sen. Dianne Feinstein, a California Democrat, criticized the sheriff, saying suspect Juan Francisco Sanchez-Lopez should have been detained.

Sanchez-Lopez says he found the gun under a bench on the pier and it accidently fired when he picked it up.

In Washington, D.C., the Senate is expected to vote Tuesday on a bill that would punish jurisdictions that don't cooperate with federal immigration agents. The White House is threatening to veto the bill, saying it would lead to mistrust between federal and local governments.

San Francisco declared itself a sanctuary city in 1989, passing an ordinance that bans city officials from enforcing immigration laws or asking about immigration status unless required by law or court order.

San Francisco and other cities and counties have routinely ignored requests from Immigration and Customs Enforcement to keep people in custody. The jurisdictions say they can't hold arrestees beyond their scheduled release dates without probable cause.

However, more than half of the roughly 340 jurisdictions that previously declined to cooperate with ICE are now doing so in some form, as long as they don't have to keep immigrants in custody.

The shift came after outreach by federal immigration officials and several high-profile cases including the one in San Francisco.

San Francisco Sheriff Ross Mirkarimi has defended the release of Sanchez-Lopez, saying deputies were following city sanctuary and due process ordinances that allow detention only under a court order targeting violent felons. He issued a department-wide memo in March prohibiting communication between his staff and ICE without approval.

One resolution to be considered Tuesday was proposed by Supervisor Mark Farrell and calls for the sheriff to rescind his ban on talking to immigration authorities. It essentially seeks more communication among local and federal authorities.

Farrell, backed by Mayor Ed Lee, said the city's sanctuary policies were never intended to protect criminals and that a blanket ban on communication erodes public safety.

The other resolution, co-sponsored by Supervisor David Campos, urges the sheriff's office not to participate in the detainer notification system that asks jails to let ICE officials know when an inmate is being released so ICE has time to pick them up.

"It's really important for the board to take a stand," Campos said.

Campos and Supervisor Eric Mar oppose the measure calling for more communication, saying it would weaken the city's sanctuary protections.