The outside check could be "a panel of three judges or one judge or something [else] that would give the American people confidence that there was, in fact, a compelling case to launch an attack against an American citizen," Robert Gates, defense chief under presidents Barack Obama and George W. Bush, told CNN's "State of the Union."
"I think that the rules and the practices that the Obama administration has followed are quite stringent and are not being abused," said Gates. "But who is to say about a future president?"
Gates, who was also CIA director from 1991-1993, said he was "a big advocate of drones," even though innocent people sometimes die in combat-drone attacks.
"But I'm saying that you have, first of all, the numbers, I believe, are extremely small," he said. "And second, you do have the ability to limit that collateral damage more than with any other weapons system that you have."
The debate over the Obama administration's use of drones broke open last week with a Senate hearing to consider John Brennan, the president's counter-terrorism chief, as CIA director.
Of particular interest to lawmakers are the legal grounds the administration used in authorizing a Sept. 30, 2011, CIA drone strike that killed Anwar al-Awlaki, a U.S.-born cleric of Yemeni descent.
U.S. officials accused Awlaki of being a leader of al-Qaida's Yemen affiliate.
Sen. Angus King, Ind-Maine, told "State of the Union" his recent proposal to create a judicial-review process for targeted Americans was not intended to slow down U.S. response time in the terrorist hunt.
"Often these strikes are planned weeks in advance," King said. "Where there is time," the administration should submit its target list "in confidence" to a court to get a ruling on whether the evidence is strong enough to go forward with a drone attack, he said.
"It just makes me uncomfortable that the president, whoever it is, is the prosecutor, the judge, the jury and the executioner all rolled into one," King said.
Sen. Rand Paul, R-Ky., said he would go further, insisting U.S. citizens on a president's kill list should get a full trial.
"I'm probably for executing you, but I would want to hear the evidence, I would want to have a judge and a jury," Paul told CNN.
"It can be fairly swift, but there needs to be a trial for treason," he said. "The president, a politician, Republican or Democrat, should never get to decide someone's death by flipping through flash cards, and say do you want to kill him? I don't know. Yeah, let's go ahead and kill him."
On the other hand, Sen. John McCain, R-Ariz., argued such matters are what presidential powers are all about and should therefore be reserved to the White House.
"I don't agree with [an outside legal process] because I think it is an encroachment on the powers of the president," McCain told "Fox News Sunday."
"But what we need to do is take the whole program out of the hand of the Central Intelligence Agency and put it into the Department of Defense, where you have adequate [congressional] oversight," he said.
"Since when is the intelligence agency supposed to be an air force of drones that goes around killing people? I believe that it's a job for the Department of Defense."
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