CAIRO—Egypt's interim military rulers on Monday agreed to let the European Union's top foreign diplomat meet with Mohammed Morsi, as concern grew for the former president's welfare nearly a month after his ouster.

Catherine Ashton, the EU's high representative for foreign affairs and security policy, would be the first person aside from military personnel to see Mr. Morsi since the army ousted him on July 3 and sequestered him in undisclosed locations. It was unclear late Monday if Mr. Morsi would meet with her. He refused...