The researchers, Mr. Ozzie said, recognized that “this issue is not going away,” and were trying to foster “constructive dialogue” rather than declaring that no solution is possible.

Mr. Savage said the talks had focused on trying to create a safe enough way to unlock data on encrypted devices, as opposed to the separate matter of decoding intercepted messages sent via encrypted communications services, like Signal and WhatsApp.

“The stuff I’ve been thinking about is entirely the device problem,” he said. “I think that is where the action is. Data in motion and the cloud are much harder to deal with.”

The deliberations shed new light on public remarks by Trump administration officials in recent months. In October, Mr. Rosenstein, the deputy attorney general, argued in a speech that permitting technology companies to create “warrant-proof encryption” was endangering society.

“Technology companies almost certainly will not develop responsible encryption if left to their own devices,” he said. “Competition will fuel a mind-set that leads them to produce products that are more and more impregnable. That will give criminals and terrorists more opportunities to cause harm with impunity.”

And Mr. Wray, the F.B.I. director, has twice given speeches this year in which he pointed to Symphony, an encrypted messaging system for banks. Pushed by a state regulator, several banks agreed to give copies of their Symphony keys to law firms. Because Symphony keeps a copy of encrypted data on its servers, that arrangement created a backup means for investigators to gain access to the messages if necessary.

“At the end, the data in Symphony was still secure, still encrypted, but also accessible to the regulators so they could do their jobs,” Mr. Wray told a cybersecurity conference in Boston this month. “I’m confident that by working together and finding similar areas to agree and compromise, we can come up with solutions to the ‘going dark’ problem.”