David Cameron says social network must explain to parents its decision to allow images showing decapitations

David Cameron has accused Facebook of being irresponsible following its decision to allow a video of a beheading to remain on its website.

The prime minister's criticism was echoed by a hostage charity, which warned of the "acute distress" such images would cause to the families of victims.

After complaints were first made about the video depicting a killing in Mexico, Facebook added captions to the front of videos warning that they contained extremely graphic content and that they "may be upsetting".

The website owners resisted suggestions the video should be taken down.

The inaction was condemned by Cameron, and Hostage UK, a charity representing the families of people who have been kidnapped and killed.

A Hostage UK statement said: "The public are well aware of the brutalities committed, and a public showing … adds nothing other than to cause further unimaginable suffering."

Cameron said Facebook should explain its decision to "worried parents". Facebook allows people to use the site from the age of 13, although many 11-year-olds join when they go to secondary school.

The shadow crime and security minister, Diana Johnson, also condemned the inaction, saying: "It is entirely unacceptable for Facebook to be hosting these disgraceful videos. Not only do they glorify violence, but they will be horrifying to people who accidentally view them. It is especially worrying to see Facebook allowing this content, given the huge number of children who are regular users. They should remove it now."

Facebook introduced a temporary ban on such videos in May but has since decided to remove the block on grounds that the site is used to share information about world events.

Hostage UK said Facebook's ban reversal was wrong. "Many of us at Hostage UK have worked with the families and friends of hostages who have been tortured and beheaded, with the execution having been recorded on video and made widely available. We know firsthand the acute distress these videos and images cause."

The charity said that it strongly urged Facebook to reconsider its decision to show the video.

Facebook has said the public should be free to view beheading videos then condemn the content; it would take a different approach if the actions in the footage were "encouraged or celebrated".

Sources close to Facebook have indicated that the company is keeping its policies under close review amid the furore over the posting of the video.

Meanwhile other Facebook rules, under the listing of "nudity and pornography", ban displays of topless photos on its site.

Stephen Balkam, a member of the Facebook safety advisory board, urged the company to rethink its policy change. He told Sky News: "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 adopt their own policies."

However, the pressure group Index On Censorship said: "The decision to show beheadings is part of a much wider debate on whether companies like Facebook should moderate the content they host. With over a billion users worldwide, Facebook's decisions about what can and can't be shown have a huge impact on global freedom of expression." A spokeswoman said: "Some of these videos are produced in a reporting context."

Padraig Reidy, a senior writer at Index On Censorship, commented: "One can see a certain logic behind not allowing pictures of bare breasts; Facebook doesn't want its platform to be given over to soft and hard porn."

While it does have a "like" button, to indicate approval, Facebook does not have a clear way for users to indicate dislike of content so it would be difficult to know how the company could measure the basis on which people viewed a video.

A spokesperson for Facebook told the Guardian: "We look at what [people] say in the comments with a clear expectation they must be condemnatory. There are a lot of videos being removed where the comments aren't [condemnatory]."

John Baptista, associate professor of information systems at Warwick Business School, said: "It is impossible to create rules for everything on the web, so I mostly believe in self regulation based on common sense and guiding principles.

"This relies on companies like Facebook being sensible and responsible, however in this case sadly I think Facebook is late in responding to feedback and it is very disappointing to see them not being proactive in addressing a serious issue such as this. I hope they do take the feedback seriously and respond positively."

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."