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With the compromise, State Department-CIA tensions began to subside. Only once or twice during Mrs. Clinton’s tenure at State did U.S. diplomats object to a planned CIA strike, according to congressional and law-enforcement officials familiar with the emails.

U.S. diplomats in Pakistan and Washington usually relayed and discussed their concur or non-concur decisions via the State Department’s more-secure messaging system. But about a half-dozen times, when they were away from more-secure equipment, they improvised by sending emails on their smartphones about whether they backed an impending strike or not, the officials said.

The time available to the State Department to weigh in on a planned strike varied widely, from several days to as little as 20 or 30 minutes. “If a strike was imminent, it was futile to use the high side, which no one would see for seven hours,” said one official.

Adding to those communications hurdles, U.S. intelligence officials privately objected to the State Department even using its high-side system. They wanted diplomats to use a still-more-secure system called the Joint Worldwide Intelligence Community Systems, or JWICs. State Department officials don’t have ready access to that system, even in Washington. If drone-strike decisions were needed quickly, it wouldn’t be an option, officials said.

Some officials chafed at pressure to send internal deliberations through intelligence channels, since they were discussing whether to push back against the CIA, congressional officials said.

The Wall Street Journal first reported on the State Department-CIA tug-of-war over the drone program in 2011.

Under pressure to address critics abroad, Mr. Obama pledged to increase the transparency of drone operations by shifting, as much as possible, control of drone programs around the world to the U.S. military instead of the CIA. An exception was made for Pakistan.

But even in Pakistan, Mr. Obama recently signaled a shift. The drone strike that killed Taliban leader Mullah Akhtar Mansour last month was conducted by the military, not the CIA, and the outcome was disclosed.

While the CIA still controls drones over the tribal areas of Pakistan near Afghanistan, the pace of strikes has declined dramatically in recent years. U.S. officials say there are fewer al Qaeda targets there now that the CIA can find.