The firms have until next week, the end of April, to tell ministers how they will cut underage use and clamp down on bullying and overuse. Hunt named Facebook, Snapchat, Twitter, Apple, Microsoft, Yahoo and Google as among those under discussion.
Hunt said that he and culture secretary Matt Hancock “will not rule out legislation where it is needed”, in an article in the Sunday Times. The feedback from the firms will feed into the governments response to the Internet Safety Strategy consultation in May.
The major social media companies have an age floor of 13, although ministers fear these are regularly flouted.
The chief medical officer, Dame Sally Davies, will review the impact of social media on childrens mental health.
Social media companies have come under increased pressure in recent months after a scandal over access to data on Facebook by Cambridge Analytica, a political consultancy alleged to have interfered with elections including the US presidential election and the Brexit vote.
Meanwhile, the health secretary has previously said social media can be as damaging to children as smoking or obesity, in a shot across the tech giants' bows in February.
Hunt today accused the firms of "turning a blind eye" to their impact on children, saying their failure to act is “morally wrong”.
The letter said: “I am concerned that your companies seem content with a situation where thousands of users breach your own terms and conditions on the minimum user age.
“I fear that you are collectively turning a blind eye to a whole generation of children being exposed to the harmful emotional side effects of social media prematurely.”
The health secretary said technology must have “safe limits”, and that industry has both the “brightest minds and biggest budgets” to tackle the issues.