Former Defense Secretary Donald Rumsfeld on Sunday questioned why the Obama administration is releasing so much information about the operation that resulted in the death of Usama bin Laden and the intelligence behind it.

While Rumsfeld praised President Obama for overseeing and green-lighting the daring raid last weekend, he suggested the White House could be taking a risk in sharing the details it has with the public.

"The more information that goes out about intelligence, the greater the risks to our people and the less likelihood we're going to be able to capture and/or kill some of the people who would result from the intelligence take here," Rumsfeld said on CBS' "Face the Nation."

Rumsfeld noted that White House officials have had to correct the record after initially bungling the details of the raid in briefings with reporters. He said the Pentagon likely wants to keep the information private.

"I would have preferred a lot less discussion out of the White House about intelligence," Rumsfeld said.

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Since last week, administration officials have held a series of briefings to go over the details of the raid, review the decade-long investigation that led to it and disclose some information about the evidence seized from the compound. The White House last week indicated it would stop providing details about the raid itself -- officials have since kept their comments mostly to the subject of the evidence being analyzed by the CIA.

Sen. John Kerry, D-Mass., chairman of the Senate Foreign Relations Committee, also said Sunday that he doesn't want to hear any more discussion about what happened on the night of the raid. He noted some questions have been raised about the fatal shooting of bin Laden, but said the Navy SEALs team did exactly what they were supposed to do.

"We need to shut up and move on about the realities of what happened in that building," Kerry told "Face the Nation."