Ian Russell’s call comes after Health Secretary Matt Hancock wrote to internet giants following the death of 14-year-old Molly Russell, telling them they have a duty to act.
Mr Hancock delivered the message after Molly’s father said Instagram “helped kill my daughter”.
The Health Secretary said he was “horrified” to learn of Molly’s death, and feels “desperately concerned to ensure young people are protected”.
In his letter to Twitter, Snapchat, Pinterest, Apple, Google and Facebook (which owns Instagram), he said: “I welcome that you have already taken important steps, and developed some capabilities to remove harmful content. But I know you will agree that more action is urgently needed.
“It is appalling how easy it still is to access this content online and I am in no doubt about the harm this material can cause, especially for young people.
“It is time for internet and social media providers to step up and purge this content once and for all.”
He added that the Government is developing a white paper addressing “online harms”, and said it will look at content on suicide and self-harm.
He said: “I want to work with internet and social media providers to ensure the action is as effective as possible. However, let me be clear that we will introduce new legislation where needed.”
Molly, from Middlesex, was found dead in her bedroom in November 2017 after showing “no obvious signs” of severe mental health issues.
Her family later found she had been viewing material on social media linked to anxiety, depression, self-harm and suicide.
Mr Russell, said the algorithms used by Instagram enabled Molly to view more harmful content, possibly contributing to her death. “I have no doubt that Instagram helped kill my daughter. She had so much to offer and that’s gone,” Mr Russell told the BBC.
He said: “It is clear to us that despite what the social media companies tell the public about their policies of removing disturbing content that such content is still available for young people to find easily and by finding it they have more and more of it pushed on them by algorithms.
“It is time for tech companies to stand up and take more responsibility for the content available to their young users.
“While many may say it is impossible to ‘police the internet’ there must be a better and safer way to control what we expose young people to on the internet and to ensure more support is offered to those looking for answers online.
“This is far too important an issue to simply dismiss as being too difficult.
“We are pleased that the Health Secretary has taken action to write to tech companies to ask for the type of content that Molly saw to be removed.
“However, I fear that the tech companies have already shown that they cannot be trusted to police this themselves and that legislation may well be needed.
“I would like to thank the HM Senior Coroner Andrew Walker for all his efforts so far in helping us try to find some answers about the role of social media in the death of our beautiful daughter Molly.”
Merry Varney, solicitor from Leigh Day representing the Russell family, said: “From what we’ve learnt in Molly’s case and the examples of how the algorithms push negative material, it surely needs fully investigating whether these platforms, which often allow users from 13 years old, are contributing to suicides and self-harm.”
A spokeswoman for Instagram said: “We are undertaking a full review of our enforcement policies and technologies around self-harm, suicide and eating disorders.
“As part of this, we are consulting further with mental health bodies and academics to understand what more we can do to protect and support our community, especially young people.
“While we undertake this review, we are taking measures aimed at preventing people from finding self harm-related content through search and hashtags.”
The Molly Rose Foundation said: “Following Molly Russell’s tragic death in 2017 Molly’s family and friends set up a charity in her memory with the aim of preventing other young people from taking their own lives.
“The Molly Rose Foundation is committed to increasing awareness of the issues surrounding suicide in people below the age of 25 and aims to help connect young people suffering with mental ill health to the support and practical advice they need.
“The charity are currently fundraising to sponsor mental health first aid and suicide awareness training for educators and other professionals working in the youth sector.”
An inquest into Molly’s death is expected later this year.