Cameron described the death of 14-year-old Hannah Smith, who hanged herself last week after receiving abuse on the website ask.Fm, as "absolutely tragic". He blasted "vile" websites that allow bullying to take place.
"There's something all of us can do as parents and as users of the Internet and that is not to use some of these vile sites," Cameron told Sky News television.
"Boycott them, don't go there, don't join them."
Ask.Fm has described Hannah's suicide as a "true tragedy" and pledged to work with police investigating her death.
The website, which is popular amongst teenagers, has a question-and-answer format and allows users to post messages without their identity being disclosed.
Hannah's father has called for the website to face murder or manslaughter charges.
Cameron urged website operators to do more to stop them from being used as forums for bullying.
"The people that operate these websites have got to step up to the plate and show some responsibility in the way that they run these websites," he said.
"I'm very keen we look at all the action we can take to try and stop future tragedies like this."
It is the ninth most popular social networking site in the world, according to data released in June by the Internet monitor comScore.
Charities have called for tighter regulation of social networks.
Internet abuse has hit the headlines in Britain in recent weeks after several women, including two lawmakers, received rape and death threats on Twitter.
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