He said the Department of Defense was actively searching for an alternative detention facility.
"This is not something, in my judgment, that we should leave to the next president," Carter told reporters at the Pentagon.
He said he and the White House were on the same page when it comes to closing the prison, as Obama promised to do before being elected and which he is now making a final push to accomplish.
"It's expensive... And not something the president wants to leave to his successor."
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He said defense officials had been assessing Fort Leavenworth, in Kansas, and the Navy Brig in Charleston, South Carolina as possible destinations for prisoners.
"We will also be assessing other sites in the coming weeks," he added.
Any transfers of the prisoners to sites within the continental United States are likely to be highly controversial in Congress, but Carter said his department is working on putting together a concrete plan for lawmakers to consider.