Obama's secretary of defense nominee has been depicted by the media as the un-Chuck Hagel; but on Israel, Carter would represent continuity.
According to Hagel, the U.S. wants to help Iraq regain the territory it lost to Islamic State militants earlier this year.
Says decision to step down was mutual.
Carter, a former deputy secretary at the Department of Defense, would replace Chuck Hagel, sources say.
Hagel has served as Secretary of Defense since February 2013; resignation comes as President Obama's national security team has been battered by multiple foreign policy crises.
President Rivlin just called Israel a 'sick society.' If he was an American politician, he'd be probably forced out of his job.
Turkey FM: Kobani corridor for arms, fighters is 'unrealistic'; Iran warns U.S.: Toppling Assad would put Israel at risk; Triple suicide attack kills 26 Kurdish officers;
U.S. defense secretary says the coalition is doing what it can from the air, but that Islamist militants still threatening Kobani.
Direct aid underscores level of U.S. concern about Islamist militants' gains in north; U.S. had previously insisted on only selling arms to Iraqi government.
Akram Abusharar, a lawyer from Michigan, claims his family's home was bombed during Operation Protective Edge in Gaza.