Harmful suicide and self-harm content online "has the effect of grooming people to take their own lives", the suicide prevention minister has said.
Jackie Doyle-Price has told the BBC that social media companies must "step up" to protect vulnerable users.
It comes after links were made between the suicide of teenager Molly Russell and her exposure to harmful content.
The government is to roll out new laws to remove illegal content and protect vulnerable people later this year.
Digital Minister Margot James promised to crack down on many of the social media platforms that have "fallen short" in their response to online bullying, abuse and misinformation.
In a speech at a conference for Safer Internet Day, Ms James said: "We will soon be publishing an Online Harms White Paper which will set out clear expectations for companies to help keep their users, particularly children, safe online.
"We will introduce laws that force social media platforms to remove illegal content, and to prioritise the protection of users beyond their commercial interests."
Meanwhile Ms Doyle-Price was due to meet Facebook on Tuesday to discuss what action it is taking.
She told BBC Breakfast: "We want social media not really to be doing this through the stick of the law, we want them to do it to look after their users."
She said she hoped senior staff at Facebook, which also owns Instagram, would act - ideally using algorithms to protect people rather than "bombard" them with advertising.
Ms Doyle-Price said: "Sometimes they do [act], but more often they don't".
Addressing the National Suicide Prevention Alliance Conference on Tuesday, she said: "If companies cannot behave responsibly and protect their users, we will legislate.
"They shouldn't wait for government to tell them what to do. It says a lot about the values of companies if they do not take action voluntarily."
Speaking to the BBC, she said: "We could use fines, we could make social media companies much more responsible and apply the full force of the law to them if we feel they are being negligent in their duty of care to their users."
The Department for Culture, Media and Sport (DCMS) and the Home Office are due to publish a white paper on the government's approach to online safety later this year.
Ms Doyle-Price said the father of Molly Russell, who took her own life in 2017 aged 14, had done much to highlight the issue.
"I am full of admiration for Molly's father for being so brave and frank," she said.
Molly's father, Ian Russell, told the BBC he believed Instagram had "helped kill my daughter".
When her family looked at her Instagram account after her death, they found distressing material about depression and suicide.
Molly case 'has focused minds'
Ms Doyle-Price said that after Mr Russell spoke out, "so many other parents have spoken out...it has really focused people's minds".
She added: "The really shocking thing is that he had absolutely no idea that his daughter was looking at these things online."
The boss of Instagram, Adam Mosseri, is due to meet the health secretary this week over the platform's handling of content promoting self-harm and suicide.
Writing in the Daily Telegraph, he said Molly's case had left him "deeply moved" and he accepted the site had work to do.
He wrote: "We rely heavily on our community to report this content, and remove it as soon as it's found.
"The bottom line is we do not yet find enough of these images before they're seen by other people."
'Hooked on self-harm'
In a separate case, Libby, 16, and her father Ian have shared their story after hearing of Molly's death.
At the age of 12, Libby, became "hooked" on posting and viewing self-harm images on Instagram - including pictures of cutting, burning and overdosing.
Her father said his family reported such images to Instagram, but the social media company did nothing.
Speaking to the BBC, Libby described how she was drawn in to an online community and recalled sharing pictures of her fresh cuts with 8,000 followers.
Read more of her story here.