By Laura Meckler, Wall Street Journal–

The Trump administration said Monday it would withhold federal criminal-justice grants from cities, counties and states that don’t fully cooperate with federal immigration authorities, a first strike in the new administration’s battle against so-called sanctuary cities.

The policy itself is no different from one announced last year by the Obama administration, which threatened to pull grants from jurisdictions that bar officials from communicating with federal agencies about immigration.

Attorney General Jeff Sessions announced Monday that he was reaffirming the more limited Obama-era policy, and implied that more sweeping rules are coming. He also said the Justice Department would try to take back previously granted funding from places that weren’t in compliance with the communications law.

“When cities and states refuse to help enforce immigration laws, our nation is less safe,” Mr. Sessions said from the White House. “I strongly urge our nation’s states and cities and counties to consider carefully the harm they are doing to their citizens by refusing to enforce our immigration laws and to rethink these policies.”

People on both sides of the debate saw the announcement as an early step in an expected crackdown on cities that refuse to cooperate with federal immigration enforcement. It is also possible that Trump officials will enforce the rule more aggressively than their predecessors did.

The rules don’t address the question at the heart of sanctuary cities: whether jurisdictions can be forced to hold undocumented inmates in jail longer than planned when federal immigration officers issue “detainers” requesting time to pick up the inmates so they can be put into deportation proceedings. President Donald Trump threatened to withhold federal grant funding from places that don’t cooperate.

Many cities and counties see their sanctuary policies as more important than ever given the Trump administration’s more aggressive deportation policies, which focus on criminal offenders but aren’t limited to that group.

“Cities seeking to comply with the Constitution and protect immigrant communities should be able to do so without heavy-handed threats from the federal government,” said Kristen Clarke, president of the Lawyers’ Committee for Civil Rights Under Law.

Details of sanctuary-city policies vary widely, but they all limit cooperation with federal immigration enforcement to some extent. Supporters say they are needed to maintain trust between immigrant communities and the police. Many city officials see deportations of low-level criminals as wrongly breaking up families that are part of their communities, and say it isn’t their job to enforce federal immigration law.

The Justice Department expects to award around $4 billion in grants through its Office of Justice Programs and its Community Oriented Policing Services office in the current fiscal year, which ends in September. A Justice Department official said the announcement was meant to reaffirm the existing policy issued last July and make clear it would be a priority going forward.

“Cities who receive our hard-earned tax dollars must be in compliance with federal immigration law,” said Rep. John Culberson (R., Texas), who said he helped persuade the Obama administration to adopt this policy last year.

No jurisdiction lost grant money for running afoul of this statute during the Obama administration, a Justice Department official said. He wouldn’t say whether the Trump administration had denied any funding based on this rule.

A report from the Justice Department’s inspector general last year found several jurisdictions whose policies likely ran afoul of the statute. That included several places that limit communication regarding undocumented inmates who Immigration and Customs Enforcement officers want detained. The report found that cities and counties don’t explicitly restrict sharing information but that the policies, as applied, may have that effect.

Gregory Chen, director of advocacy for the American Immigration Lawyers Association, reads the statute more narrowly and said it doesn’t apply to communication about inmates and when they will be released. He said the announcement was meant to “intimidate the hundreds of localities across the country which are in fact complying with the law.”

—Aruna Viswanatha contributed to this article.

Write to Laura Meckler at laura.meckler@wsj.com