Facebook has begun adding warning messages to videos on its site showing decapitations and other instances of extreme violence.
The alert states: "Warning! This video contains extremely graphic content and may be upsetting."
The move follows its decision to allow the clips to be posted to its site following a temporary ban on the material, introduced in May.
The prime minister and Facebook's own advisors had criticised the decision.
The social network said that it wished to allow its users - who can be as young as 13 - to share and condemn the material. It added that it would continue to block clips if the original poster glorified or celebrated the violence shown.
On Monday the firm said it might, in time, add warnings or other controls, but initially allowed a recently uploaded decapitation clip to appear unaltered.
This prompted David Cameron to tweet: "It's irresponsible of Facebook to post beheading videos, especially without a warning. They must explain their actions to worried parents."
US charity the Family Online Safety Institute - a member of the social network's Safety Advisory Board - also raised concern saying it had not been alerted to the change of policy despite previously stating such videos "crossed the line".
A spokeswoman for Facebook declined to comment about its latest move.
She had previously defended its decision to allow a video showing a woman being beheaded - believed to have been filmed in Mexico - to be shared despite the fact it bans images and videos showing a woman's "fully exposed breast".
"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," she said.
"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."
A UK member of Facebook's Safety Advisory Board said he still had concerns despite the addition of the warnings.
"It's a step forward but it's still horrific content," said Will Gardner, chief executive of Childnet.
He added that he needed to look into the changes before commenting further.
Until Monday Facebook had also featured adverts alongside the video of the Mexican murder despite the fact several users had complained to it about the material.
Car-sharing firm Zipcar, whose service was one of those shown, said it was disappointed by the discovery.
"We want you to know that we do not condone this type of abhorrent content being circulated on Facebook," it said in a statement.
"We have expressed to Facebook in the past the critical need to block offensive content from appearing and we will continue to engage with them on this important matter."
Facebook has since disabled Zipcar and other firms' ads from appearing on the page in question.
One of the Facebook accounts that had requested the death video be removed belongs to the South Australia Police force (Sapol).
It said it had been contacted by a member of its local community about the matter.
Shelaye Boothey, director of Sapol's media and public engagement section, told the BBC: "Ultimately this is a decision that Facebook is entitled to make, however anyone concerned with the publishing of the video should continue to express their concerns through the appropriate Facebook channels."
Hostage UK - a charity that supports kidnap victims and their families - added that it was also urging Facebook to reconsider its decision.
"We know first-hand the acute distress these videos and images cause and we stress that this continues to be a source of worry to the families of today's hostages," it said.
"We can see no useful purpose being served by the decision to make such recordings available. The public are well aware of the brutalities committed and a public showing of such material adds nothing, other than cause further unimaginable suffering."
However, some freedom of speech campaigners believe that Facebook should not block the videos, even if they do celebrate the violence contained.
French digital rights group La Quadrature Du Net described the actions as "privatised censorship".
"It plays a profoundly anti-democratic role when it makes any such choice, whatever the limits are and whatever the good reasons it uses to make the decision," said the organisation's co-founder Jeremie Zimmermann.