The U.S. Department of Justice says Harvard University puts Asian-American applicants at a disadvantage through the school’s use of a subjective “personal rating” in the admissions process, according to a new court filing in a federal lawsuit challenging the legality of affirmative action.

The statement of interest filed Thursday by the Justice Department supported the claims made by the plaintiffs, who have sued Harvard for allegedly limiting the number of Asian-American students it admits and holding them to a higher standard...