Dunford, testifying Thursday before a Senate committee holding hearings on his confirmation, said some U.S. forces are likely to stay in the country after NATO withdraws, The Washington Post reported.
The Senate is expected to act quickly on Dunford's confirmation. He is to succeed Marine Gen. John Allen as commander of the International Security Assistance Force, the U.S. and NATO mission in Afghanistan.
Dunford said more than 1,000 soldiers would be needed in Afghanistan after 2014 but did not specify a number.
Allen, who has been appointed commander of U.S. forces in Europe, was supposed to appear with Dunford at a joint confirmation hearing. Obama asked the Senate to wait on confirming Allen after he became entangled in the sexual scandal that forced retired Gen. David Petraeus to resign as director of the CIA.