It provoked a sharp backlash in some moderate suburban communities as well as in some more conservative areas upstate. Several county officials refused to comply or sued to stop the law, though it proved popular in liberal enclaves like New York City.

During negotiations over the bill, which passed by a slim majority in the State Senate, Mr. Cuomo had expressed concerns over federal immigration officials gaining access to D.M.V. records, something that the bill broadly forbade, without a court order.

“They’re using that personal data that they get from that database to look up an individual’s date of birth, their photo. They’re using that as they build that case,” Mr. Wolf told the Fox News anchor Tucker Carlson on Wednesday night as he announced the action. “They can no longer do that because of what New York did.”

But the state’s attorney general, Letitia James, supported the bill’s passage, saying it was constitutional and contained “ample protections for those who apply for driver’s licenses.” She promised to defend it if it were challenged.

Activists and immigrants also celebrated the bill, contending that the ability to obtain a driver’s license was crucial to surviving. Many lined up outside D.M.V. offices after the legislation took effect in December.

Mr. Wolf said that the action was the result of “an initial assessment” and that the department would review its response going forward.