Mr. Obama decided to accelerate the attacks — begun in the Bush administration and code-named Olympic Games — even after an element of the program accidentally became public in the summer of 2010 because of a programming error that allowed it to escape Iran’s Natanz plant and sent it around the world on the Internet. Computer security experts who began studying the worm, which had been developed by the United States and Israel, gave it a name: Stuxnet…

Told it was unclear how much the Iranians knew about the code, and offered evidence that it was still causing havoc, Mr. Obama decided that the cyberattacks should proceed. In the following weeks, the Natanz plant was hit by a newer version of the computer worm, and then another after that. The last of that series of attacks, a few weeks after Stuxnet was detected around the world, temporarily took out nearly 1,000 of the 5,000 centrifuges Iran had spinning at the time to purify uranium…

An error in the code, they said, had led it to spread to an engineer’s computer when it was hooked up to the centrifuges. When the engineer left Natanz and connected the computer to the Internet, the American- and Israeli-made bug failed to recognize that its environment had changed. It began replicating itself all around the world. Suddenly, the code was exposed, though its intent would not be clear, at least to ordinary computer users.

“We think there was a modification done by the Israelis,” one of the briefers told the president, “and we don’t know if we were part of that activity.”

Mr. Obama, according to officials in the room, asked a series of questions, fearful that the code could do damage outside the plant. The answers came back in hedged terms. Mr. Biden fumed. “It’s got to be the Israelis,” he said. “They went too far.”