American women should be required to register for the draft, two top military officials said Tuesday, following the Pentagon's decision to open all jobs including elite commando positions to females.

Though the US military has been an all-volunteer force since near the end of the Vietnam War, in 1973, all men aged 18-25 must nonetheless register for the draft in case of a national crisis and re-institution of conscription.

After Pentagon chief Ashton Carter in December announced a "No Exceptions" decision to unlock every occupation in America's vast military to women, lawmakers and observers have wondered if it is only fair they register for the draft, too.

Speaking at a Senate Armed Services Committee hearing, top generals from both the Army and the Marine Corps said it was time for women to be eligible for the so-called selective service.

"It's my personal view that, based on this lifting of restrictions for assignment ... that every American who's physically qualified should register for the draft," said General Robert Neller, the commandant of the Marine Corps.

Army General Mark Milley made a similar statement, saying "all eligible and qualified men and women should register for the draft."

Some gender equality advocates argue the current law is sexist, and a men's-rights group in San Diego is suing the government to change it.

Currently, the government website through which young men sign up retains its male-only language telling people to register.

"It's what a man's got to do. It's quick, it's easy, it's the law," the site states, while noting there has been no decision to require females to be subject to a future military draft.

Democratic Senator Claire McCaskill, who raised the issue at the hearing, said she would like to see women register.

"Asking women to register as we ask men to register would maybe possibly open up more recruits as women began to think about ... the military is an option for me," she said.

Milley noted that the first female recruits would likely arrive for infantry and armored basic training at the Army's Fort Benning in Georgia in the fall.