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 terror threats, but 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 and catalogued Muslims in New York who adopted new, Americanized surnames. NYPD spokesman Stephen Davis confirmed Tuesday that detectives assigned to the unit had been transferred to other duties within the department’s Intelligence Division.

Linda Sarsour, the executive director of the Arab American Association of New York, said she was among a group of advocates at a private meeting last week with police at which the department’s new intelligence chief, John Miller, first indicated the unit — renamed the Zone Assessment Unit — wasn’t viable. She applauded the decision but said there’s still concern about the police use of informants to infiltrate mosques without specific evidence of crime.

“This was definitely a part of the big puzzle that we’re trying to get dismantled,” Sarsour said. But, she added, “This doesn’t necessarily prove to us yet that these very problematic practices are going to end.”