Hate speech, terror recruitment videos and sexual images of children all took too long to be removed, said the Home Affairs Select Committee report.
The government should consider making the sites help pay to police content, it said.
But a former Facebook executive told the BBC the report "bashes companies" but offers few real solutions.
The cross-party committee took evidence from Facebook, Twitter and Google, the parent company of YouTube, for its report.
It said they had made efforts to tackle abuse and extremism on their platforms, but "nowhere near enough is being done".
The committee said it had found "repeated examples of social media companies failing to remove illegal content when asked to do so".
It said the largest firms were "big enough, rich enough and clever enough" to sort the problem out, and that it was "shameful" that they had failed to use the same ingenuity to protect public safety as they had to protect their own income.
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