CAIRO, July 10 (Reuters) - Egypt's prosecutor's office ordered the arrest on Wednesday of Muslim Brotherhood leader Mohamed Badie on charges of inciting violence outside the Republican Guard headquarters where 55 people were killed on Monday, state news agency MENA reported.

Other senior Brotherhood officials were also ordered held, including Badie's deputy Mahmoud Ezzat and party leaders Essam El-Erian and Mohamed El-Beltagi.

Thousands of Brotherhood followers have been maintaining a vigil near a mosque in northeast Cairo demanding the reinstatement of Mohamed Mursi, toppled as president by the army last week. (Reporting by Tom Perry; Writing by Peter Graff; Editing by Alison Williams)