WASHINGTON — After last week’s tragic news that an errant CIA drone strike had mistakenly taken out an American and an Italian hostage in Pakistan, critics of the spies’ program — who have long argued the targeted killings should strictly fall in the military’s wheelhouse — are rallying to finally take the drone trigger out of the agency’s hands.

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“Having a covert program gives the Obama administration maybe more flexibility,” said Rachel Stohl, a senior associate at the Stimson Center who works on drone and armament issues. “I’m not sure that they would characterize it as being outside the rules.”