A suburban New York county that recently barred residents from wearing masks is now making an exception for police officers so they can obscure their identities while helping the federal authorities detain immigrants.

Bruce Blakeman, the Nassau County executive, announced the new policy at a news conference on Friday, saying he had signed an executive order amending a county law that bans the wearing of masks in public except for religious or medical reasons.

Under the amended law, all federal, state and local law enforcement officers operating in the county, on Long Island, can wear face coverings when it is “necessary to protect their personal safety, the personal safety of their families or the integrity of the operation.”

Mr. Blakeman, a Republican, said the change did not apply solely to immigration actions, and he cast it as a safety measure meant to keep protesters from tracking down the personal information of police officers and agents from Immigration and Customs Enforcement, or ICE.

The move comes as Democratic lawmakers in California and New York are pushing to ban the wearing of masks by federal agents, including those working for ICE, in many circumstances.

The issue of ICE agents taking people into custody while wearing unmarked uniforms and balaclavas to conceal their faces has become a major point of conflict amid the Trump administration’s immigration crackdown, with critics saying it smacks of authoritarianism.