Hagel said that he is in favor of “exploring options and seeing what is the best.”
Petraeus announced last month that he would also be assuming the role of visiting professor at City University of New York’s Macaulay Honors College.
The DoD is currently faced with cutting $41 billion from its current budget.
President Obama has repeatedly said that the use of chemical weapons would be a “game changer” for the United States.
Hezbollah has denied responsibility for the incursion into Israeli airspace.
Hagel has already visited Jordan and will follow with stops in Saudi Arabia and the United Arab Emirates.
The Senate Majority Leader says another potential ricin-laced letter has been discovered at an Air Force base in Washington, D.C.
The Army personnel will consist of largely planners, replacing a similar number of United States forces that have been in Jordan for several months.
Hagel will travel to Israel, Jordan, Saudi Arabia, Egypt and the United Arab Emirates.
Defense Secretary Chuck Hagel promised his Israeli counterpart, Defense Minister Ehud Barak, in March that the DoD will continue to support the defense missile system.