Hobby Lobby’s president Steve Green said he is in the process of repatriating 11,500 antiquities to the Iraqi and Egyptian governments, bowing to what he called justified criticism from scholars and authorities over the ways he amassed a vast collection for the Museum of the Bible in Washington, D.C.

Mr. Green, who is also chairman of the museum’s board, said the Bible museum is helping his family collection coordinate the return of around 5,000 ancient papyrus fragments and 6,500 ancient clay objects because the artifacts...