Gen. David Petraeus, who handed over command on Tuesday to Gen. Raymond Odierno, will lead US Central Command.
Improved security has boosted optimism, but US commanders want to be assured it is "irreversible."
Top US commander in Iraq said Thursday he is likely to recommend further drawdowns before leaving his post in the fall.
The move brings greater focus to the conflict in Afghanistan. Lt. Gen. Odierno is set to succeed Petraeus in Iraq.