Three White House national security officials were given some details about the operation, dubbed Fast and Furious. The operation allowed firearms to be illegally purchased, with the goal of tracking them to Mexican drug cartels. But the effort went out of control after agents lost track of many of the weapons.

The supervisor of the Bureau of Alcohol, Tobacco, Firearms and Explosives operation in Phoenix specifically mentioned Fast and Furious in at least one email to a White House national security official, and two other White House colleagues were briefed on reports from the supervisor, according to White House emails and a senior administration official.

But the senior administration official said the emails, obtained Thursday by The Times, did not prove that anyone in the White House was aware of the covert “investigative tactics” of the operation.