Sen. Dianne Feinstein called on the city of San Francisco to participate in a federal immigration law enforcement program after the murder of 32-year-old woman in the city, allegedly at the hands of an illegal immigrant who had seven felonies and had been deported five times, but was released by the sheriff's office without telling the federal government.

The powerful senator from California, the top Democrat on the Intelligence Committee who also sits on the Judiciary panel, urged San Francisco to commit to participating in the Department of Homeland Security's new Priority Enforcement program, which focuses federal immigration enforcement efforts on convicted criminals and public-safety threats.

After looking into the circumstances surrounding the tragic killing of Kathryn Steinle, Feinstein said the San Francisco sheriff's office should have complied with an Immigration and Customs Enforcement detainer asking it to keep the alleged shooter in custody. Juan Lopez-Sanchez, an illegal immigrant who had been convicted of 10 crimes, is the alleged shooter, and was quickly detained after the shooting.

"I strongly believe that an undocumented individual, convicted of multiple felonies and with a detainer request from ICE, should not have been released. We should focus on deporting convicted criminals, not setting them loose on our streets," Feinstein said, adding that she is looking into whether additional federal legislation is necessary.

Feinstein has written to San Francisco Mayor Edwin Lee suggesting he participate in the DHS's Priority Enforcement Program, as the Los Angeles County Board of Supervisors agreed to do in a recently adopted resolution.

"This program will enable federal law enforcement to better cooperate with state and local counterparts to take custody of individuals who pose a danger to public safety before they are released," she said.

In addition, Rep. Duncan Hunter, R-Calif., will introduce a bill restricting funding to local municipalities that refuse to comply with federal immigration requests, "known as sanctuary cities."

Hunter's measure would deny federal funds for cities with so-called sanctuary policies in place. Specifically, the bill would restrict money from the State Criminal Alien Assistance Program, or SCAAP, which reimburses states and localities for the costs of detaining illegal immigrants with criminal records.

In an interview with a local ABC affiliate, Sanchez admitted he chose to return to San Francisco because it was a sanctuary city with lax immigration enforcement policies.

"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 in a statement. "One program that most certainly should cease reimbursement is SCAAP, which is intended to mitigate the costs of incarceration and extend salaries and overtime."

"And we should look into other programs too, but there should be wide support for a response, such as this proposal, that exercises a constitutional prerogative of Congress in order to uphold the law," he added.

Earlier Tuesday, a DHS official with U.S. Immigration and Customs Enforcement testified before a Senate committee and blamed the San Francisco sheriff's office for the murder because they ignored a DHS request to keep Sanchez in custody.

But the official also said the federal government did not intervene and take him into custody in anticipation of deporting him because it has a policy of pursuing all outstanding criminal warrants against a subject before deporting him.

"In that particular case, the gentleman had an outstanding felony narcotics warrant, and we feel strongly that the Bureau of Prisons made the right decision in trying to resolve that criminal warrant before we were allowed to take further civil action," said Philip Miller, an ICE official.