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House Judiciary Committee Chairman Bob Goodlatte, Virginia Republican, said the department’s policies resulted in “immigration-enforcement free zones.”

“The end result of DHS’s practices is that the American people have lost all confidence in this administration’s willingness to enforce our current immigration laws or use any enhanced enforcement tools that Congress may give it,” Mr. Goodlatte said. “This in turn has made it exceedingly difficult for Congress to fix our broken immigration system.”

Mr. Smith and other Republicans asked Mr. Johnson about more than 36,000 immigrants with criminal records who were released into communities last year while awaiting deportation.

Among those immigrants were dozens charged with murder, kidnapping and other major charges.

Even as Mr. Johnson was testifying, the House voted 218-193 to dedicate $5 million to fund a study of the releases. Rep. Steve King, the Iowa Republican who wrote the amendment, asked Mr. Johnson whether he would comply with the review. The secretary said he would.

The $5 million study still must survive Senate scrutiny before it becomes law.

While Republicans demanded more enforcement, Democrats pleaded with Mr. Johnson to curtail Secure Communities, a program created by the George W. Bush administration but dramatically expanded under President Obama.

The program takes fingerprints that localities run through the FBI and checks them against immigration databases to determine whether the person being checked is an immigrant eligible to be deported.

Backers, including the Obama administration, have argued that it’s an efficient way to identify the kinds of criminal immigrants the president has said he wants to target for deportation.

Some mayors and state lawmakers have balked, saying they believe the program scoops up lower-level criminals and that it’s hurting the ability of state and local police to work with immigrant communities.

More than five dozen localities and states have adopted policies saying that they won’t comply with the program — chiefly by ignoring requests to hold immigrants for pick-up by U.S. Immigration and Customs Enforcement officers.

When it came to Deferred Action for Childhood Arrivals, Mr. Johnson told one lawmaker that administration officials are making decisions “on an individual basis,” screening each illegal immigrant for eligibility. He said case-by-case determinations are critical for it to be considered prosecutorial discretion.

But Mr. Johnson later told another lawmaker that they “can’t have a case-by-case judgment made with respect to how we’re going to administer this program.”