Facebook has bowed to public pressure and agreed to ban clips showing people being decapitated after its stubborn refusal to do so was criticised by its own safety advisory board.

Two videos were posted on the website last week showing decapitations that appeared to originate in Mexico. The first showed two victims admit to being drug smugglers for a Mexican cartel before being attacked with a chainsaw and knife in front of the camera. Another one-minute long video showed a woman being beheaded by a masked man.

The social network had initially told a university student who reported the videos on Monday that they did not “violate Facebook's Standard on graphic violence”. Then an online petition demanding the videos removed has launched and  accumulated more than 400 signatures this week.

“This is not a petition against Facebook as an organisation, I am merely making this petition in order to protect its users,” it said.

The US-based Family Online Safety Institute (FOSI) said the graphic nature of the violence in the videos meant the material had “crossed a line” and called on Facebook to remove them on Wednesday.

The FOSI is one of five leading safety organisations on the Facebook Safety Advisory Board which meets to discuss “issues related to online safety”.

“Personally and professionally I feel that Facebook has got this call wrong,” said Stephen Balkam, the organisation's chief executive.

Mr Balkam told the BBC: “You've just got to consider would this go out on daytime television news? I don't think it would, even with a warning saying this is something you may want to avoid. It crosses a line.”

John Carr, who sits on the executive board of the British Government's Council on Child Internet Safety, claimed the US-company must have “taken leave of their senses”. He added: “I hate to think how an unsuspecting youngster might react if they saw it through their news feed or in any other way. This is just wrong at every level.”

It a statement Facebook the videos would raise public awareness of “action or causes”. But within two hours it agreed to delete the videos.

“We will remove instances of these videos that are reported to us while we evaluate our policy and approach to this type of content,” Facebook said.

On Wednesday the company reported a 38 per cent increase in its first-quarter revenue to £937million with an average of 665million people using the site a day in March.