Mr. Comey made no reference to that report in an hourlong speech and discussion at the Brookings Institution, and White House officials have said they are still struggling to come up with a policy for Mr. Obama to adopt.

While Apple and Google declined to respond to Mr. Comey’s speech, just last week, at an event in Palo Alto, Calif., executives of several companies made clear they would not slow their efforts to offer encryption. In fact, they said, the effort would accelerate, and they would develop algorithms that would take the government months or years to crack, and then insist that consumers themselves create their own encryption keys so that the companies would be unable to crack the code or provide it to the government.

Colin Stretch, the general counsel for Facebook, called encryption “a key business objective” for technology companies. “I’d be fundamentally surprised if anybody takes the foot off the pedal of building encryption into their products,” he said.

Mr. Comey’s complaint is that technology is vastly outpacing the ability to assure that authorities can track suspects however they communicate — by cellphone, text message or over a smartphone app. Four years ago the F.B.I. pressed to update a 20-year-old law that required traditional communication providers — like AT & T or Verizon — to build into their systems an ability to immediately comply with wiretap orders.

But many different companies, including small start-ups and foreign firms, now transmit communications. The F.B.I.’s effort to require many kinds of companies to provide unencrypted, plain-text information to the government if served with a court order failed. Last year the F.B.I. called back its proposal so that companies would still be permitted to offer messaging that would be entirely encrypted between users.

The Snowden disclosures about the surveillance carried out by the National Security Agency killed all those proposals. Now Mr. Comey appears to be going even further, seeking a way into data stored on phones even if it is never transmitted. And he wants to make sure that Apple, or other phone manufacturers, do not “throw away the key” that allows that information to be unencrypted. The companies, meanwhile, are going the other way: They want to convince customers that their data will be private, even from the phone’s maker.

“Just as people won’t put their money in a bank they won’t trust, people won’t use an Internet they won’t trust,” Brad Smith, the general counsel for Microsoft, said recently.