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Other lawmakers seemed leery of the program’s current reach even as they lined up against the oversight proposals.

Sen. John McCain, Arizona Republican, said a Feinstein-backed oversight panel would be “an encroachment on the powers of the president of the United States.”

“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 oversight,” Mr. McCain 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.”

And Rep. Tom Cole, Oklahoma Republican, questioned whether America’s intelligence operations were benefiting from the killings.

“We are losing a lot of opportunities out there to actually extract people and get information,” he said. “Human intelligence is really much more important than taking out individual targets.”

During Thursday’s hearing, Mr. Brennan defended drone strikes only as a “last resort,” but he said he had no qualms about going after Anwar al-Awlaki in September 2011. A drone strike in Yemen killed al-Awlaki and Samir Khan, both U.S. citizens. A drone strike two weeks later killed al-Awlaki’s 16-year-old son, a Denver native.

“I think it’s very unseemly that a politician gets to decide the death of an American citizen,” said Sen. Rand Paul, Kentucky Republican. “They should answer about the 16-year-old boy, al-Awlaki’s son, who was killed not as collateral damage, but in a separate strike.”

Those strikes came after U.S. intelligence concluded that the elder al-Awlaki was senior operational leader of al Qaeda in the Arabian Peninsula plotting attacks on the United States, including the failed Christmas Day bombing of an airplane landing in Detroit in 2009.

Lawmakers largely sided with the strategy even if they differed on how precisely to execute it.

“If you take up arms against America and you fight in a terrorist training camp or on the front lines in Pakistan or Afghanistan or Yemen, you shouldn’t be surprised if America reaches out and exacts justice against you,” said Republican Rep. Tom Cotton, Arkansas Republican, who opposes bringing judges into the decision-making process.

Mr. Durbin appeared on NBC’s “Meet the Press.” Mr. King, Mr. Gates and Mr. Paul spoke with CNN’s “State of the Union.” Mr. Rogers was interviewed on CBS’ “Face the Nation.” Mr. McCain and Mr. Cotton were on “Fox News Sunday.” Mr. Cole was a guest on ABC’s “This Week.”