Defense Secretary Hagel is considering a 21-day "quarantine-like" policy for all troops returning from West Africa, the Pentagon said Tuesday.

The proposal was recommended to Hagel on Tuesday by the Joint Chiefs of Staff — which consists of its chairman Gen. Martin Dempsey and the chiefs of staff of the Army, Navy and Air Force.

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Earlier this week, the Army Chief of Staff Gen. Ray Odierno ordered all soldiers returning from West Africa to undergo a 21-day isolation and enhanced monitoring period.

Odierno "has done this out of caution to ensure soldiers, family members and their surrounding communities are confident that we are taking all steps necessary to protect their health," the Army said Monday.

The Pentagon said Hagel supports that "initial decision" but would take his time deciding whether or not to expand that policy department-wide.

Currently, a dozen soldiers from U.S. Army Africa are being isolated and monitored at Vicenza, Italy, including its commander Maj. Gen. Darryl Williams. The Pentagon has said there was no event to trigger the policy.

Pentagon press secretary Rear Adm. John Kirby acknowledged that implementing a department-wide quarantine-like policy goes farther than what President Obama and the Centers for Disease Control and Preventions have recommended, but said Hagel would not stand in the way of the Army's decision, or any other service if they should implement that policy.

On Monday, Air Force officials at the Ramstein Air Base in Germany also implemented stricter measures for airmen coming back from West Africa, including possibly quarantining troops on a case-by-case basis.

There are currently about 880 troops in West Africa, training healthcare workers, building Ebola treatment units and mobile labs, and airlifting medical supplies and providing other logistical help.