The U.S. Anti-Doping Agency asked a federal judge to dismiss a lawsuit filed by Lance Armstrong, the latest volley in a fight between the former cyclist and the body that polices drugs in American sports.

The filing, made late Thursday, comes 10 days after lawyers working on behalf of Mr. Armstrong refiled a suit against USADA in federal court in Austin, Texas, in an effort to stop the agency from pursuing a case against him. The case against Mr. Armstrong could strip him of his seven Tour de France titles and bar him from...