Obama and former the Massachusetts governor and GOP presidential nominee met for lunch privately at the White House to discuss the U.S. leadership position in the world and the importance of maintaining that position.
The men dined on white turkey chili and southwestern grilled chicken salad, the White House said.
At his first news conference after the election, Obama said he wanted to meet with Romney to discuss ways they could work together on this nation's problems.
"There're certain aspects of Governor Romney's record and his ideas that I think could be very helpful," Obama said during a Nov. 14 news conference, citing in particular Romney's success in running the Salt Lake City Olympics.
White House spokesman Jay Carney Wednesday said he had no information on whether Obama is considering Romney for a Cabinet post now that the shuffle is under way.
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