"The fight against terrorism and hate speech has to be a joint one," the spokesman said. "The government and the security services are doing everything that they can, and it's clear that social companies can and must do more."
Earlier this week, Google vowed to better police its website after several companies deserted the internet giant for failing to keep their adverts off hate-filled videos. Facebook and others have also been criticised for not doing enough to moderate content on their platforms.
The comments from May's office echo those of Foreign Secretary Boris Johnson, who on Thursday said internet providers and social media companies have "got to look at the stuff that's going up on their sites, they've got to take steps to invigilate it, to take it down where they can."
May, a former interior minister who spent six years before she became prime minister putting in place policies to try and prevent the radicalisation of British citizens, has consistently urged social media firms to take a tougher stance.
"We don't want this material to appear in the first place and when it does appear we want it to be taken down as quickly as possible," May's spokesman said.
"The ball is now in their court, let's see how they respond."
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