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Cause of Action, a government accountability group, also called for Mr. Edwards to resign, pointing to their own efforts in July to urge Mr. Obama to remove him.

“Inspectors general are required to act as internal agency watchdogs to save taxpayers’ money, investigate corruption and punish wrongdoing,” said Executive Director Dan Epstein in a statement. “Unfortunately, Edwards has failed to do his job on all fronts.

NOTE: An earlier version of this story incorrectly attributed comments to Carlton Mann, chief operating officer for the Department of Homeland Security’s Inspector General. Mr. Mann did not make any statements about the job status of Homeland Security Inspector General Charles Edwards.