Story highlights Two of the U.S. military service chiefs believe women should now be required to register for the draft

The comments come after the Defense Department opened up all combat jobs to women

(CNN) Two of the U.S. military service chiefs believe women should now be required to register for the draft after the Defense Department opened up all combat jobs to women.

Marine Corps Commandant Gen. Robert Neller and Army Chief of Staff Gen. Mark Milley agreed that the current policy, which requires only males register for the Selective Service System, should be changed after restrictions that barred women from trying out for combat jobs were lifted last year.

"Every American who's physically qualified should register for the draft," said Neller at a Senate Armed Services Committee hearing Tuesday that examined the new policy to admit women into combat units.

"I think that all eligible and qualified men and women should register for the draft," Milley added.

Secretary of the Navy Ray Mabus and Army Acting Secretary Patrick Murphy, also testifying at the hearing. would not go as far but did say they believed the issue should be put to a national debate.

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