SAN FRANCISCO—A U.S. national labor agency is investigating two charges against tech giant Apple Inc. filed by employees, records on its website show. The charges, filed on Aug. 26 and Sept. 1, are being reviewed by the U.S. National Labor Relations Board’s office in Oakland, California. The agency declined to comment. “We take all concerns seriously and we thoroughly investigate whenever a concern is raised,” Apple, which is based in Cupertino, California, said in a statement that cited employee privacy in declining to discuss specifics. Ashley Gjovik, a senior engineering program manager at Apple, told Reuters that she filed the Aug. 26 charge, which cites harassment by a manager, reduction of responsibilities, and increases in unfavorable work, among other complaints. The Sept. 1 charge was filed by Cher Scarlett, an Apple software engineer who said the company repeatedly stopped discussions of pay among employees. The documents she sent the agency, …