Facebook (Nasdaq: FB) is tightening restrictions on graphic content, altering its rules after a recent video on the site of a beheading incited an uproar.

“When we review content that is reported to us, we will take a more holistic look at the context surrounding a violent image or video,” the Menlo Park, California-based company said yesterday on its website. Facebook said it “will remove content that celebrates violence.”

Facebook will also consider whether the person posting the content is being responsible by only sharing with age- appropriate users and by providing a warning alongside the clip.

Facebook announced Tuesday it was working on new ways to keep users from stumbling across gruesome content on its website following an outcry over the discovery of beheading videos there.

The controversy — which has drawn critical comment from British Prime Minister David Cameron — illustrates the difficulty of setting a universal standard across the social network used by 1 billion people. Facing sharp criticism, Facebook Inc. issued a statement clarifying that violent videos were only allowed if they were presented as news or held up as atrocities to be condemned.

“If they were being celebrated, or the actions in them encouraged, our approach would be different,” the company said in a statement. “However, since some people object to graphic video of this nature, we are working to give people additional control over the content they see. This may include warning them in advance that the image they are about to see contains graphic content.”

The company came under fire after the BBC reported Facebook users were showing a violent video that included a beheading earlier this week. Facebook said it has re-examined some recent graphic images and taken them down.

“It’s irresponsible of Facebook to post beheading videos, especially without a warning,” U.K. Prime Minister David Cameron wrote on his Twitter account following the reports. “They must explain their actions to worried parents.”

With more than a billion users on the site, Facebook is adding features to encourage greater interaction among members, while trying to maintain some control over what gets shared.

The company has already put in place some restrictions on content, such as videos posted for “sadistic pleasure,” Facebook said. Users can still share clips that are “of public interest or concern, such as human rights abuses, acts of terrorism, and other violence,” the company said.

Wooing Media Companies 

In other news, Facebook is testing a feature to simplify how media companies find content to post on its service, stepping up efforts against Twitter Inc. for driving traffic to news providers.

The new tool suggests stories from media sites such as Time.com that could be posted on Facebook after the articles show high engagement with users, the company said today in a blog post. The feature takes a more proactive stance in proposing content to post, whereas Facebook previously offered data on what stories were performing well on the site.

The Menlo Park, California-based social network, which has more than 1 billion users, is looking for new ways to attract content from media and news organizations, especially as Twitter has become a hub for catching breaking news and commenting on the issues of the day. Twitter is set to go public soon.

“People come to Facebook to not only see and talk about what’s happening with their friends but also read news and discover what is going on in the world around them,” Facebook said in the post. “Because of this, we work closely with media organizations.”

Facebook said referral traffic from its service to media sites has increased by more than 170 percent on average in the past year. The company also touted results of a recent test that showed 29 media sites boosted referral traffic by more than 80 percent when they posted more often on the service.