Coinbase said the emails were "not the result of malicious behaviour".

Two-factor authentication requires users to enter information, such as a texted code, in addition to a password.

And the alert caused alarm many among users, who feared their accounts had been hacked.

Under most circumstances, only someone with access to the account could change two-factor authentication settings.

"I got the reply and panicked someone accessed my account or made withdrawals," one user tweeted.

'Building trust'

The company said the error had been due to an issue with its notification system.

Coinbase apologised on social media, saying it was focused on building trust and "that issues like this can hurt that trust".

And a post from a moderator support account on Reddit suggested the company was "crediting a small number of users" affected with $100 (£73) worth of Bitcoin.

Coinbase has experienced rapid recent growth, telling CNBC, in June, its more than 43 million registered users at the end of 2020 had grown to 68 million.