NEW YORK — New York City Mayor Zohran Mamdani and local officials from across the country filed a federal lawsuit Monday seeking to block a Trump administration rule that would broaden how immigration officials evaluate whether someone could become a “public charge.” The rule, scheduled to take effect Friday, would give federal officials greater authority to consider an immigrant’s use of Medicaid and food assistance when deciding whether to approve certain green-card or visa applications. The administration argues the changes are permissible under immigration law; the cities and counties challenging the policy say it exceeds the legal limits on public-charge determinations. New York City is leading the municipal coalition, which includes Chicago, San Francisco, Santa Clara County in California, Seattle and King County in Washington. The case was filed in the U.S. District Court for the Southern District of New York. A second lawsuit is being brought by a coalition led by New York Attorney General Letitia James. The parallel challenges reflect concerns among state and local officials that the rule could discourage eligible immigrants from using health care, nutrition assistance and other public programs, even when those services do not affect their immigration status. Mamdani said the policy could make immigrant families afraid to seek medical care or use food assistance to which they are legally entitled. He also warned that the uncertainty could spread beyond people directly covered by the rule, causing eligible families to avoid benefits and creating broader public-health and economic consequences for New York. The lawsuits come as cities and states face the local costs of providing health and social services while having little control over federal immigration decisions. The legal fight will now turn on whether the administration’s expanded interpretation is consistent with federal law and prior court decisions governing public-charge reviews.