WhatsApp is allowing users to encrypt their backed-up chats, making them unreadable without access to a password or 64-digit encryption key.

Facebook, the messaging app’s owner, said from Thursday some users would be able to fully encrypt messages stored on Google Drive or Apple’s iCloud. The company said it would be introducing the feature slowly to people with the latest version of WhatsApp.

The move comes against a backdrop of concern about the safety of backed-up messages. In May, WhatsApp sued the Indian government over new IT laws that include putting messages into a traceable database. The government would then be able to identify and act against the sender if any content was ruled unlawful. India is WhatsApp’s largest market.

Facebook said users could hold their own encryption key, preventing a scenario whereby a cloud service provider could be forced to hand the key to authorities. It said: “You can now secure your end-to-end encrypted backup with either a password of your choice, or a 64-digit encryption key that only you know. Neither WhatsApp nor your backup service provider will be able to read your backups or access the key required to unlock it.”

WhatsApp messages sent and received on mobile devices are already end-to-end encrypted, with the latest feature designed to reassure people who back up their messages on cloud services in case they lose their phone. The feature can be activated by opening the app’s settings, tapping on chats, then chats backup and end-to-end encrypted backup.

Facebook’s plans gradually to introduce end-to-end encryption across its suite of services, which also include Instagram and Facebook Messenger, have previously been criticised by the government. The home secretary, Priti Patel, has said it would put children at risk and offer a hiding place for abusers and other criminals.

In June, the Home Office said the government was in favour of strong encryption to protect citizens from harm online but was concerned that Facebook’s implementation of the technology would blind law enforcement’s ability to access content.

WhatsApp’s more than 2 billion users send more than 100bn messages a day. Speaking in September, when the proposal was announced, to the US technology blog The Verge, WhatsApp’s chief executive, Will Cathcart, said: “I believe strongly that governments should be pushing us to have more security and not do the opposite.”

Mark Zuckerberg, Facebook’s chief executive, also speaking in September, said: “WhatsApp is the first global messaging service at this scale to offer end-to-end encrypted messaging and backups, and getting there was a really hard technical challenge that required an entirely new framework for key storage and cloud storage across operating systems.”