"These are not the values upon which I was raised or those of my family," the group quoted him as saying.
The committee, in a statement on its website, said Emanuel told Oakar it was unacceptable to make such remarks against any ethnic or religious group.
Oakar welcomed the apology, saying: "We cannot allow Arabs and Muslims to be portrayed in these unacceptable terms."
Some analysts in the Middle East have raised concerns about the appointment of Emanuel, who has a record of strongly supporting Israel, suggesting he could use his position to influence Obama's policies in the region.
Emanuel dismissed the suggestions earlier this week, saying Obama did not need his influence to "orientate his policy toward Israel".
Benjamin Emanuel is a Jerusalem-born doctor who was active in the Irgun - an underground Zionist organisation that fought the British in Palestine prior to the founding of Israel in 1947.