The bureau counted 260 strikes by Predator and Reaper drones since President Obama took office, and it said that 282 to 535 civilians had been “credibly reported” killed in those attacks, including more than 60 children. American officials said that the number was much too high, though they acknowledged that at least several dozen civilians had been killed inadvertently in strikes aimed at militant suspects.

A senior American counterterrorism official, speaking on the condition of anonymity, questioned the report’s findings, saying “targeting decisions are the product of intensive intelligence collection and observation.” The official added: “One must wonder why an effort that has so carefully gone after terrorists who plot to kill civilians has been subjected to so much misinformation. Let’s be under no illusions — there are a number of elements who would like nothing more than to malign these efforts and help Al Qaeda succeed.”

Getting a full picture of the drone campaign is difficult. It is classified as top secret, and Obama administration officials have refused to make public even the much-disputed legal opinions underpinning it.

But Mr. Obama spoke about the program in an online appearance last week.

“I want to make sure that people understand: actually, drones have not caused a huge number of civilian casualties,” he said in the forum on YouTube. “For the most part they have been very precise precision strikes against Al Qaeda and their affiliates.” He called the strikes “a targeted, focused effort at people who are on a list of active terrorists.”

However, American officials familiar with the rules governing the strikes and who spoke on the condition of anonymity said that many missiles had been fired at groups of suspected militants who are not on any list. These so-called signature strikes are based on assessments that men carrying weapons or in a militant compound are legitimate targets.