Choking back tears, parents whose children were slain by illegal immigrants said Tuesday the federal government and so-called sanctuary cities both share blame for their children’s deaths, and pleaded with Congress for an all-out effort to secure the border and deport those who already snuck in.

“I don’t want your sympathy, I want you to do something,” demanded Laura Wilkerson, whose 18-year-old son was strangled, had his throat smashed and his body lit on fire by an illegal immigrant trained in mixed martial arts. “Quit sitting silent because it’s going to help you get a vote.”

The lawmakers, who said they were moved by the testimony of Ms. Wilkerson and a handful of others who recounted their relatives’ murders, vowed to take action and trained much of their criticism on San Francisco, whose sanctuary policy protected an illegal immigrant whom police have accused of killing 32-year-old Kathryn Steinle earlier this month as she walked on Pier 14 with her father.

The city’s former mayor, Sen. Dianne Feinstein, California Democrat, announced she’s working on a bill to punish cities that refuse to cooperate with federal authorities trying to deport serious criminals, and one of the country’s top police chiefs testified to Congress that policies like San Francisco’s aren’t considered good practice among the police community.

But President Obama’s top lieutenants on immigration, who sat through the moving testimony from the victims’ families, still rejected their calls to get tough on sanctuary cities, insisting that asking for cooperation has already won over some jurisdictions and could still work on San Francisco too.

“I’m hopeful I don’t have to hit somebody over the head with the federal hammer,” Sarah Saldana, director of U.S. Immigration and Customs Enforcement, said.

Tuesday’s hearing grew heated at one point as the victims’ families were leaving the witness table and Ms. Saldana and her counterpart, U.S. Citizenship and Immigration Services Director Leon Rodriguez, took their seats.

Don Rosenberg, whose son was killed by an illegal immigrant in a drunken driving incident, but who was not on the witness panel, stepped forward and scolded sanctuary city defenders.

“How dare you!” he said in remarks that appeared to be addressed to the Rev. Gabriel Salguero, pastor of Lamb’s Church of the Nazarene in New York City, who defended sanctuary policies.

Mr. Rosenberg continued to admonish the sanctuary city defenders as Judiciary Committee Chairman Chuck Grassley banged his gavel and demanded order. Mr. Rosenberg was escorted out of the room by U.S. Capitol Police, trailed by a horde of reporters and photographers.

The rest of the hearing was calmer, but no less intense, with Ms. Wilkerson recounting the graphic details from the autopsy report on her son, Joshua, and Jim Steinle recounting his daughter’s final words to him moments after she was shot and fell to the ground: “Help me, Dad.”

The man accused in that shooting, Juan Francisco Lopez-Sanchez, had been deported five times before and was still being sought by Ms. Saldana’s ICE agents — but the federal Bureau of Prisons had shipped him to San Francisco instead on a decades-old drug warrant.

San Francisco authorities decided not to pursue the drug case, but rather than turn Sanchez over to ICE, which had put a detainer request on him, the county sheriff’s department released Sanchez as per its sanctuary policy. Under that policy, the sheriff won’t even inform ICE when an illegal immigrant is about to be released, shielding them from being picked up by agents.

Now, in the wake of the killing and the growing political pressure to do something, the sheriff and the city’s mayor are exchanging letters over whether the sanctuary policy can be changed under city law.

Ms. Feinstein, a senior Democratic senator who was the city’s mayor in the 1970s and 1980s, has sided with the mayor and called for the sheriff to change his policy. She also said she’s writing legislation to force cities and counties to cooperate when ICE is trying to deport felons.

“The man who killed Kate is a classic case of multiple felonies and prior deportations, and a simple phone call would have been enough,” Mrs. Feinstein said.

Tom Manger, chief of police in Montgomery County, Maryland, and head of the Major City Chiefs Association, said refusing to even notify federal authorities of an illegal immigrant’s release is not considered good practice on the part of police agencies.

He said his association’s model policy calls for notification of arrests and releases, and said that’s the policy his own county follows as well. But he also said local police shouldn’t be asked to go further and enforce immigration laws themselves.

“Surely no member of the committee would want to hear from their own community that we did not respond to a call for help because we were off enforcing immigration laws,” he chided the Judiciary Committee in his written testimony.

The hearing highlighted a shift in the immigration debate. Over the last few years, immigrant rights advocates have essentially won the public debate, focusing on sympathetic illegal immigrants, and so-called Dreamers in particular, who have made good on their chances of a better life in the U.S.

But enforcement supporters had argued that gave a one-sided portrayal of the issue and insisted illegal immigration wasn’t a victimless crime. Tuesday’s hearing put an exclamation point on those claims.

“I want you to be angry that America’s borders are wide open. America does not know who is in this country. It is time to put Americans first,” Ms. Wilkerson said. “Close the borders, figure out who is really here. Keep statistics. Realize that we are at war right here in this country.”

Republicans, joined by some Democrats, are vowing to take up the fight.

The House will vote later this week on a bill by Rep. Duncan Hunter, California Republican, to withhold funding from several federal grant programs from any cities that refuse to cooperate on immigration.

Mr. Grassley said he’s working on his own bill that would not only withhold funding from sanctuary cities but also impose a mandatory 5-year federal prison sentence on any illegal immigrant who sneaks back in after having been deported.

Ms. Saldana said she would oppose that, saying it’s “just too low-level an offense” for federal prosecutors to worry about.

“To expand it to just illegal entries or re-entries would be a very big problem for us,” she said.

As for legislation punishing sanctuary cities, she repeatedly said she would look at whatever Congress writes but would prefer they leave the matter to her and let her try to cajole reluctant cities and counties to cooperate.

She said her new Priority Enforcement Program (PEP), which replaced the previous controversial Secure Communities program, is winning over local jurisdictions.

Where Secure Communities demanded local police hold illegal immigrants beyond the time they’d otherwise be released, the PEP instead asks that police notify ICE ahead of time so agents can be on hand when illegal immigrants are to be set free. That is so agents can pick them up immediately, but the localities don’t have to hold them any longer than they would otherwise.

Mr. Grassley also prodded Mr. Rodriguez over Mr. Obama’s 2012 tentative deportation amnesty, and one case in particular, where an illegal immigrant granted amnesty was later accused of four murders in North Carolina. Mr. Rodriguez has admitted the man had gang ties that should have prevented him from being approved for the amnesty.

But when Mr. Grassley demanded to know who had been fired over the incident, Mr. Rodriguez said nobody had been cut loose. Instead, he said, employees had been “counseled” on how to apply the amnesty so gang members don’t get approved. He also said his agency had rechecked hundreds of thousands of amnesty recipients to weed out other gang members.

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