ROME (AP) — Defense Secretary Ash Carter sounded like he's nearly made up his mind about opening all combat jobs to women, as he told U.S. troops in Sicily on Tuesday that limiting his search for qualified military candidates to just half the population would be "crazy."

Meanwhile, in memo obtained by The Associated Press, Carter gave the chairman of the Joint Chiefs of Staff until the end of October to forward his review of the services' recommendations on which jobs — if any — should remain closed to women. The chairman, Gen. Joseph Dunford, was commandant of the Marine Corps until recently and was the only service chief to recommend that some front-line combat jobs stay male-only, according to several U.S. officials.

Speaking to a crowd of troops that included a large number of Marines, Carter said he hasn't decided on the recommendations sent to his office and to Dunford. He pledged to thoroughly review the recommendations, particularly those of the Marine Corps, but said that generally he believes that any qualified candidate should be allowed to compete for jobs.

"You have to recruit from the American population. Half the American population is female," Carter told the troops at Naval Air Station Sigonella in Sicily, in response to a question from a Marine. "So I'd be crazy not to be, so to speak, fishing in that pond for qualified service members."

For that reason, he said the military should recruit women into as many specialties as possible.

In the memo to all the service secretaries and chiefs, Carter said that he is "fully committed to removing unnecessary barriers to service" in the military, and he asked Dunford to review all the reports and send his final recommendation to Carter by Oct. 31.

But Carter also said that he wants to hear from everyone before he decides.

"I am less interested in who is making a particular recommendation and more interested in the reasoning behind it," he said. "My ultimate decision regarding any exception to policy will be based on the analytic underpinnings and the data supporting them."

According to officials familiar with the process, Dunford submitted a report about five-inches thick outlining why he believes women should not be allowed to compete for certain Marine infantry and front-line jobs.

Navy Secretary Ray Mabus forwarded Dunford's recommendation but also included his own conclusion that the Navy would open all jobs to women, and that he did not agree with Dunford's conclusion. The Marine Corps is a separate service within the Navy.

The Air Force and Army also did not seek to keep any jobs closed to women — including Army infantry. And, officials said that U.S. Special Operations Command determined that it will rely on the military services to send qualified candidates to compete for the jobs, which can include the Navy SEALs and Army Special Forces. The elite commando units decided that while there are concerns about women serving in the nation's most grueling military posts, they would leave it up to the services to decide who could compete.

The officials spoke on condition of anonymity because they were not authorized to discuss publicly the private reports.

The contentious issue — including the disagreement between the Navy and Marine Corps — has played out publicly. The Marines released part of their review's conclusions and Mabus has been vocal in his criticism of the Marine decision. Carter's latest memo tries to limit those tensions, warning the services that any further public discussion of the process would not be "helpful or prudent."

The Marine Corps said it did extensive research, including comparisons of all-male and mixed gender units. The units went through a lengthy testing program where they were evaluated on a variety of combat tasks.

They concluded that mixed-gender units are not as capable as all-male units, and that women often couldn't carry as much weight or shoot as well as the men. Allowing women to compete for ground combat jobs, they determined, would make the Marine Corps a less-efficient fighting machine.

Navy Rear Adm. Brian Losey, commander of the Navy's special warfare units, had many of the some concerns, but reached a different conclusion. In a memo, he said putting women in the commando jobs is not expected to increase the units' ability to fight in combat and could take focus away from readiness. But he concluded that allowing all qualified candidates to test themselves against the standards was the right thing to do.

Commanders have stressed that they will not reduce or change the standards for any of the military jobs.