A Manhattan judge hearing a lawsuit by public-housing tenants ordered the New York City Housing Authority on Tuesday to conduct lead inspections in thousands of apartments where young children live.

The preliminary injunction by the judge, Carol R. Edmead of State Supreme Court, marked the latest victory for tenant leaders who sued the authority after revelations last November that the agency had not conducted all of the lead paint inspections mandated by federal and local law.

After the lapses became public in a report by the city’s Department of Investigation, the Housing Authority acknowledged it had falsely certified lead paint paperwork with the federal government from 2013 to 2016.

Nycha, as the Housing Authority is known, has about 176,000 units. In issuing the injunction, Justice Edmead said the agency must identify the thousands of apartments that required annual lead inspections from 2013 to 2016 and inspect them within 90 days.