SAN DIEGO (CNS) - The city of San Diego works cooperatively with federal immigration authorities despite its inclusion in online lists of so-called "sanctuary cities," the mayor's office said Wednesday.

San Diego and nearby National City both appear on lists of sanctuary cities in California. The designation has been embroiled in controversy since a woman was fatally shot last week in San Francisco, which touts itself as such a city, in which officials limit their cooperation with federal immigration agencies.

The suspect in the case, an undocumented felon who has been deported five times, said he was in San Francisco because of its immigration policies.

Awbrey said San Diego and San Francisco are different cases. The San Diego Police Department "works cooperatively with federal agencies," he said.

Officials in National City did not immediately return a message seeking comment. In 2006, then-Mayor Nick Inzunza proclaimed National City to be an immigrant sanctuary.

Meanwhile, a San Diego-area congressman is poised to introduce legislation that would reduce federal reimbursements to sanctuary cities.

Rep. Duncan D. Hunter, R-El Cajon, said his bill would prevent cities that flout federal immigration laws from receiving funding under the State Criminal Alien Assistance Program, which mitigates costs for of incarceration, and extends to salaries and overtime.

"States and cities that refuse to enforce federal immigration laws directly undermine enforcement efforts and -- as recent events have shown -- present a real danger to citizens," Hunter said.

"If a state or one of its cities wants to call itself a sanctuary and deliberately ignore the law, then Congress shouldn't hesitate to withhold federal funding until there's compliance," Hunter said. "One way we show we're serious is by hitting localities where it hurts -- and that's the purse."

His bill would make states or political subdivisions of states ineligible for funding if they have "in effect any law, policy or procedure in contravention" of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996.

States, counties or cities would also be ineligible for SCAAP funding if they prohibit state or local law enforcement officials "from gathering information regarding the citizenship or immigration status, lawful or unlawful, of any individual," under the proposed legislation.

The woman who died, 32-year-old Kathryn Steinle, was shot on the San Francisco Pier, a popular tourist spot. The San Francisco Sheriff's Department has been heavily criticized for releasing the alleged gunman, Juan Francisco Lopez-Sanchez, from jail in April without notifying immigration officials.

Sheriff's officials said there was no active warrant or judicial order regarding the man.