The cabinet minister said online hate has “poisoned public life” as she pledged to bring in sweeping reforms in memory of Conservative colleague Sir David Amess.
Ms Dorries said the government had decided to re-examine its upcoming Online Safety Bill in the light of Sir David’s death.
Writing in the Daily Mail, the culture secretary said social media giants “need to hand over the data more quickly and rapidly remove the content themselves … this bill will force platforms to stop amplifying hateful content via their algorithms.”
She added: “And here’s the bottom line. If social media companies fail in any of those duties, they’ll face a financial hammer blow. Ofcom will be able to fine them up to 10% of their annual global turnover.”
The government has stopped short of committing to criminal sanctions for social media bosses with its bill – although a criminal offence has been included as a “deferred power” if tech firms fail to live up to their new responsibilities.
Recently-appointed to lead the Department for Digital, Culture, Media and Sport (DCMS), Ms Dorries is thought to be keen on pushing further than her predecessor Oliver Dowden with changes to the bill.
In a signal she intends to take a tougher stance, she wrote: “But big tech can – and must – do more right now. These are some of the most technologically sophisticated, wealthiest companies in the world.”
Ms Dorries added: “They have the tools to tackle hatred. Too many times, they’ve jeopardised people for profit. Enough is enough. Social media companies have no excuses. And once this bill passes through parliament, they will have no choice.”
The promise to bring in big fines for failures to act comes as Twitter’s UK boss said the Online Safety Bill needs more clarity.
Katy Minshall, head of UK public policy for the social media network, said fines would create an “almost existential” threat to social media platforms.
She told the BBC’s Westminster Hour programme the Bill would hand Ms Dorries “unusual powers” to change regulator Ofcom’s code of practice that would be used to regulate the likes of Facebook and Twitter.
She said the Bill had posed important questions such as “how do we define legal but harmful content” and “what sorts of exemptions should we make for journalistic content or content of democratic importance”.
Ms Minshall said: “These are questions that parliament needs to answer,” adding that banning anonymity online would “fail to deal with the problems of online abuse”.
Earlier this week, Labour leader Sir Keir Starmer challenged Boris Johnson over sanctions for tech bosses, claiming the bill in its current form would not mean criminal penalties.
Mr Johnson insisted that new internet safety laws would impose “criminal sanctions with tough sentences” on firms allowing “foul content” on their platforms.
Speaking at PMQs on Wednesday, the prime minister vowed to “bring [the bill] forward before Christmas”. But Commons leader Jacob Rees-Mogg told MPs the draft scrutiny committee would have to report back in December before the legislation could be brought forward.
Meanwhile, Ms Dorries said the killing of Sir David last week may not have been stopped by a crackdown on online abuse, but it had highlighted the threats faced by people in the public eye.
The cabinet minister revealed she had faced horrific abuse, including one person “saying they wanted to see me trapped in a burning car, and watch ‘the flames melt the flesh on my face’”.
She added: “If you’re in the public eye, and particularly if you’re a woman, death threats and online abuse are the backdrop to your daily life. It’s a dark, foreboding cloud that follows you everywhere you go.”
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