The Conservatives have promised to give users the right to delete posts from Twitter and Facebook made before they turned 18 if they win the general election.
The move is designed to give teenagers and adults more control over what information they have online.
Under the plans, social media firms will also have to take action to stop search terms directing users to inappropriate sites.
It is hoped the move will stop children accidentally stumbling on porn, with some adult channels featuring x-rated videos that have titles which play on the names of well-known films and characters.
Theresa May said that the internet had brought “a wealth of opportunity, but also significant new risks which have evolved faster than society's response to them".
She said: “We want social media companies to do more to help redress the balance and will take action to make sure they do.”
Among these measures are penalties for web giants who fail to stop children accessing harmful content, and a “comply or complain” system which will require internet companies to take down content that has been the subject of complaints.
Liberal Democrat former Cabinet minister Alistair Carmichael said: "It is certainly bold of the Conservatives to boast how they can protect people on the internet the day after the NHS has been hacked with a loophole apparently built by the US Government.
"Government and technology companies must do more to find a real solution to problematic content online but having a government agency deciding what constitutes acceptable free speech isn't it.
"We need to be working with technology companies to address the problem of hate speech, not pretending it's an easy problem that can be solved with a press release."
Additional reporting by Press Association.
