WASHINGTON—Turkey’s government used a Washington law firm to gather information about its critics, including residents of the U.S., who it believed were allied with a movement that President Recep Tayyip Erdogan regards as a central enemy, according to documents reviewed by The Wall Street Journal.

The information, gathered at the behest of the Turkish Embassy in Washington, was transmitted to public prosecutors in Turkey, according to two Turkish government memorandums marked “secret.” Activists said they fear the data is...