But an Anonymous spokesman told AFP that even heads of the group were uncertain how seriously to take the threat since the loosely-knit organisation doesn't have a strict command structure and members mask their identities.
"I found groups of people who say we absolutely are and have a trick up our sleeves," said the spokesman. "I found others that say it isn't us and that this is stupid."
The video displayed a gray image of the Anonymous logo as a digitally masked voice announced a plan to destroy Facebook and called for others to join in the cyber attack.
The video accused Facebook of holding onto the data people post in accounts and of even sharing some of it with law enforcement agencies.
"Join the cause and kill Facebook for the sake of your own privacy," the speaker urged in the video, which has been viewed more than a million times since being posted three weeks ago.
A cadre within Anonymous was evidently trying to rally cyber warriors in a Facebook attack, but the plan did not have the backing of the majority of the group, according to the spokesman.
A message on an "Anonops" account at microblogging service Twitter acknowledged that some members of the group were organising a Facebook attack but that didn't mean the sentiment was unanimous.
"This could be as dumb as one person making a video or as big as someone having already broken into the Facebook network," said the Anonymous spokesman.
Facebook declined a request for comment.