Campaigners rejected the company's claim that the move would allow users to condemn the images.
David Cameron accused Facebook of being "irresponsible" while Downing Street said that the Prime Minister thought the videos should be removed.
Facebook introduced a temporary ban in May but has now decided to remove the block.
The company says it cannot ignore the fact that the site is used to share information on world events, including acts of terrorism and human rights abuses.
However, videos and photos will still be removed if they "glorify violence".
Stephen Balkam, a member of the Facebook safety advisory board, urged the company to rethink the change in its policy.
He said: "They have some very strict rules about nudity, about sex and even about violence too.
"I just think in this case they really need to rethink how they use and how they adopt their own policies."
The Prime Minister said that the social network must explain its decision to allow images showing decapitations to "worried parents" and accused the company of being "irresponsible".
Mr Cameron's official spokesman added: "The Prime Minister's view is that the videos shouldn't be there so I think he does think that the company should address this problem."
But a Facebook spokeswoman said: "Facebook has long been a place where people turn to share their experiences, particularly when they're connected to controversial events on the ground, such as human rights abuses, acts of terrorism and other violent events.
"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."