The move comes in the wake of much-publicised password hacks at other networking sites including LinkedIn and eHarmony, the Daily Mail reported.
Millions of Facebook users have already seen a link at the top of their desktop news feed requesting them to follow 'simple security tips'.
Those that click on the link are led to the site's security page where they are asked to pick a unique password and given a tutorial on how to spot an online scam.
They are then requested to provide their phone number for secure account recovery.
This, Facebook claims, works because when a user confirms their phone number it allows the site to automatically wipe their password in the event of their account being hacked.
The social network would then send a text message to the user informing that their password has been changed.
This, the site reasons, would be preferable to sending the user and email because many of these are ignored as assumed junk and get deleted.
Facebook today said the desktop security message, already seen by millions of users in the US, will be on all accounts in the next few days.
However, it claims that the security update has nothing to do with the recent LinkedIn hack.
The social network for professionals, LinkedIn admitted to being hacked, but did not reveal the exact figure, although 6.5 million of its 161 million users' passwords appeared online on a website.
The website added that the lists published online only contained passwords and not logins, but that in all probability any hacker would have them too.
And California-based eHarmony, one of the world's most popular online dating websites, also admitted earlier this month that the personal passwords of some of its customers were hacked and posted online.
The company, which has over 20 million registered users, confirmed that passwords had been compromised but did not reveal the exact number, although some technology experts have put the figure at 1.5 million.
