Social media companies need to "purge" the Internet of harmful content that promotes self-harm and suicide, said the health secretary.
Matt Hancock delivered the message after the father of a teenager who took his own life said that Instagram "helped kill my daughter."
The minister has written to a series of Internet giants after the death of Molly Russell, 14, who tells them they have the duty to act.
Hancock said he was "horrified" to learn from Molly's death and felt "desperately worried to ensure that young people are protected."
In his letter, he said: "I am pleased that you have already taken important steps and have developed some capabilities to eliminate harmful content. But I know you will accept that more action is needed urgently.
"It's terrible how easy it is to have access to this content online and I have no doubt about the damage that this material can cause, especially for young people.
"It is high time that Internet providers and the social media intensify and purge this content once and for all."
He added that the government is developing a white paper on "online damages", and said it will analyze content on suicide and self-harm.
He said: "I want to work with Internet and social media providers to ensure that the action is as effective as possible. However, let's make sure that we will introduce new legislation when it is necessary ".
Molly was found dead in her bedroom in November 2017 after showing "no obvious signs" of serious mental health problems.
Her family later found that she had been seeing material in social networks linked to anxiety, depression, self-injury and suicide.
Molly's father, Ian Russell, said algorithms used by Instagram allowed him to see more harmful content, possibly contributing to his death.
Russell, a television director, told the Sunday Times: "It's a mystery. She went to sleep so happy. What could have caused her? The only one that had access was her two electronic devices. unleashed it
A spokesman for Instagram said that "it does not allow content that promotes or glorifies eating disorders, self-injury or suicide and that it works hard to eliminate it."
He added: "However, for many young people, discussing their mental health trip or connecting with other people who have fought similar problems is an important part of their recovery.
"That's why we do not remove any content and, on the other hand, we offer users to consult it, or publish it, to support it when they need it".
An investigation into the death of Molly is expected later this year.