The top U.S. Marine Corps and Army generals said on Tuesday that women should be required to register for the military draft, along with men, as the armed forces move toward integrating them fully into combat positions.

"I think that all eligible and qualified men and women should register for the draft," Gen. Robert Neller, the commandant of the Marine Corps, told a Senate Armed Services Committee hearing on women in combat.

Gen. Mark Milley, the chief of staff of the Army, also backed registration for women, although two other witnesses, Navy Secretary Ray Mabus and Acting Army Secretary Patrick Murphy, said only that there should be a discussion of legislation requiring women to register for the Selective Service.