In a press conference announcing his withdrawal, Gregg said he gradually came to the conclusion that his views with the administration were too different for him to accept the role.
Hagel eventually joined with moderates and progressives in the chamber to press for an early withdrawal from Iraq, though he had originally voted in favor of the resolution to invade the country.
In Washington, White House press secretary Scott McClellan said the withdrawal of some of the 157, 000 troops in Iraq is likely after this month's elections there.