Hosny is accused of making a number of public declarations described as anti-Semitic, such as his statement last year that he would personally burn any Israeli book found in the library of Alexandria.
Hosny faced eight other candidates for the post. Irina Bokova of Bulgaria received eight votes, while Austria's Benita Ferrero-Waldner, the EU External Relations Commissioner, and Russian Deputy Foreign Minister Alexander Yakowenko both drew seven votes.
The next round of voting is scheduled for Friday. A total of five rounds can be held if no one receives a majority. The winner must be confirmed during a General Assembly Oct 15.