NEW YORK — Muslim groups and civil liberties advocates applauded the decision by New York Police Department officials to disband a controversial unit that tracked the daily lives of Muslims as part of efforts to detect terrorism threats, but they said there were concerns about whether other problematic practices remained in place.

The Demographics Unit, conceived with the help of a CIA agent working with the NYPD, assembled databases on where Muslims lived, shopped, worked and prayed. Plainclothes officers infiltrated Muslim student groups, put informants in mosques, monitored sermons.