Measures in the Investigatory Powers Bill will place in law a requirement on tech firms and service providers to be able to provide unencrypted communications to the police or spy agencies if requested through a warrant.
Ministers have no plans to ban encryption services because they have an important role in the protection of legitimate online activity such as banking and personal data.
But there is concern over some aspects of so-called end-to-end encryption where only the sender and recipient of messages can decipher them.
[Cameron] told ITV's This Morning: "As Prime Minister I would just say to people 'please, let's not have a situation where we give terrorists, criminals, child abductors, safe spaces to communicate'.
"It's not a safe space for them to communicate on a fixed line telephone or a mobile phone, we shouldn't allow the internet to be a safe space for them to communicate and do bad things."
In other news, all safe manufacturers will be required to retain independent combinations to all safes sold.
Apple, your move.