According to screen shots on media sites, the social media giant was adding warnings saying such videos contained "extremely graphic content" and "may be upsetting."
Facebook had introduced a temporary ban on videos of beheadings in May following complaints that the graphic footage could cause users long-term psychological harm.
But it confirmed on Monday that it had reversed the decision on the grounds that the site is used to share information about world events, including terrorist attacks and human rights abuses.
It added, however, that it was considering adding warnings to graphic videos and that photos or videos that "glorify violence" would be removed.
British Prime Minister David Cameron on Tuesday condemned Facebook as "irresponsible" and said "worried parents" needed to hear an explanation from the US-based website.
"It's irresponsible of Facebook to post beheading videos, especially without a warning," Cameron said on Twitter.     

Facebook said that this week that it would allow such material because people are sharing this video on Facebook to condemn it.
"If the video were being celebrated, or the actions in it encouraged, our approach would be different," the statement said.
Facebook has been criticized for allowing this type of violence while banning other content such as nudity.    

On its standards page, Facebook said, "We remove content and may escalate to law enforcement when we perceive a genuine risk of physical harm, or a direct threat to public safety. Organizations with a record of terrorist or violent criminal activity are not allowed to maintain a presence on our site."
The world's biggest social network, with over one billion members, said that it seeks to avoid censorship and its policy notes that "graphic imagery is a regular component of current events, but must balance the needs of a diverse community."


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