The request was made in a letter signed by US Attorney General William Barr, British home secretary Priti Patel and Australian minister for home affairs Peter Dutton.
"We are writing to request that Facebook does not proceed with its plan to implement end-to-end encryption across its messaging services... without including a means for lawful access to the content of communications to protect our citizens," said a copy of the letter obtained by AFP and dated October 4.
The letter called on Facebook and other companies to make sure messaging systems were not so well-encrypted that law enforcement couldn't see "content in a readable and usable format" when needed.
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The request, addressed to Facebook chief Mark Zuckerberg, raises anew the conflict between technology firms intent on protecting user privacy by scrambling messages with encryption, and government agencies contending that doing so would let wrongdoers hide their schemes.
The leading social network already encrypts WhatsApp messages from end-to-end -- meaning only the sender and recipient can read the message, which is saved in encrypted form -- and is working to extend the technology to other apps in its family, including Messenger.
End-to-end encryption protects the messages of over a billion people every day, according to Facebook.
"It is increasingly used across the communications industry and in many other important sectors of the economy," Facebook said in response to an AFP query.
"We strongly oppose government attempts to build backdoors because they would undermine the privacy and security of people everywhere."
During a live-streamed question session with employees, Zuckerberg said the company recognised the challenge in balancing privacy with fighting crimes such as child exploitation and terrorism, and was working with authorities to get it right.
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"Having the availability to look at the content is a useful signal, and when you lose that you are fighting that battle with at least a hand tied behind your back and you hope there is a lot of good stuff you can do with your other hand," Zuckerberg said.
He felt the scale was still tipped toward encryption, which can help protect journalists, political protesters, and others.
Privacy has been a sore point for Facebook, and users have been clamoring for encryption of messages, according to Zuckerberg.
Clues such as patterns of behavior and connections between accounts can be used as signals of illicit behavior even if data in messages can't be seen, he noted.
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