Facebook has refused to remove a clip from its site that the NSPCC said showed a "terrified, sobbing baby" being repeatedly dunked into a bucket of water.
Facebook does not believe the video breaches its rules.
The charity has written to the UK government asking it to intervene.
"While the welfare of this child is naturally paramount we would also urge you to look at all available options which will ensure UK citizens, including millions of children, are no longer exposed to this kind of dreadful and disturbing content," the National Society for the Prevention of Cruelty to Children's chief executive Peter Wanless wrote.
"The NSPCC believes we have now reached the long overdue point where it is time for social networking sites to be held to account for the content on their sites and pay more attention to their safeguarding duties to protect children and young people, whether they are viewing the content or appearing in it."
He sent the letter to the Culture Secretary Ed Vaizey and the Minister for Internet Safety Joanna Shields.
A spokeswoman for the government confirmed the letter had been received and would be responded to in due course.
Facebook acknowledged that the video is "upsetting and disturbing", but said its users should still be able to watch it.
"In cases like these, we face a difficult choice: balancing people's desire to raise awareness of behaviour like this against the disturbing nature of the video," said a spokeswoman for the firm.
"In this case, we are removing any reported instances of the video from Facebook that are shared supporting or encouraging this behaviour.
"In cases where people are raising awareness or condemning the practice, we are marking reported videos as disturbing, which means they have a warning screen and are accessible only to people over the age of 18."
The video - running to nearly two minutes in length - showed the baby being twisted by her arms and held upside down from her legs as she is picked up and partly submerged in the water dozens of time. She cries at first but stops after the carer changes the way she is holding the infant.
The NSPCC describes the act as "callous" and "dreadful".
Although the social network now shows a warning message - known as an interstitial - at the start of the video, it was not added when the clip was initially reviewed, and the BBC had asked why one was not present.
Facebook first introduced interstitials at the end of last year, after coming under pressure to do so by one of its own safety advisers.
The Family Online Safety Institute (Fosi), had raised concerns that disturbing videos were spreading via the site and auto-playing in users' feeds without warning.
Fosi is still pressing for Facebook to let users add interstitials themselves.
Prime Minister David Cameron previously criticised the social network after it refused to remove another clip, which showed a woman being decapitated.
"It's irresponsible of Facebook to post beheading videos, especially without a warning. They must explain their actions to worried parents," he tweeted in 2013.
The US-based site, which permits anyone aged 13 and above to be a member, later issued new community guidelines explaining that it wanted people to be able to raise awareness of controversial topics.
"Sometimes, those experiences and issues involve violence and graphic images of public interest or concern, such as human rights abuses or acts of terrorism," it stated.
However, the NSPCC maintained that Facebook is not doing enough to protect children and said it is not the only online service at fault.
The charity wants the government to create a new organisation "armed with the legal powers to ensure internet companies are transparent and accountable".
"Over the last two years, under the leadership of the Prime Minister, the government partnership with industry has taken major strides in tackling child sexual abuse images on the internet.
"Google, Microsoft and other companies have prioritised this issue," Mr Wanless wrote.
"It is now time for the light to be shone on the responsibilities of social media companies, an area where progress has been extremely slow.
"As you know, the government convened a meeting of the social media companies to look at these issues in February 2014 but there has been no substantial progress since then.
"We have just re-elected a new government and now is the time for a renewed mandate and focus."
A leading child protection charity has demanded Facebook and other social networks be held to account following a clash over a "disturbing" video.