The perpetrators told the BBC Russian Service that they had details from a total of 120 million accounts, which they were attempting to sell, although there are reasons to be sceptical about that figure.
Facebook said its security had not been compromised.
And the data had probably been obtained through malicious browser extensions.
Facebook added it had taken steps to prevent further accounts being affected.
The BBC understands many of the users whose details have been compromised are based in Ukraine and Russia. However, some are from the UK, US, Brazil and elsewhere.
The hackers offered to sell access for 10 cents (8p) per account. However, their advert has since been taken offline.