Theresa May will warn Facebook, Google and Twitter they face hefty fines unless they block terrorist propaganda from appearing online.
The prime minister will be among a group of world leaders who will challenge the internet giants to develop fixes that will take down terror material within one to two hours.
In a special meeting in New York on Wednesday, they will tell internet companies they have one month to show they are taking serious action to limit the availability of terrorist propaganda.
Interior ministers from the G7 group of leading nations will then meet in Rome on October 20 to decide whether enough progress has been made.
And governments are making clear they are ready to take legislative action, which could include fines for internet giants which fail to act.
In her keynote speech to the United Nations General Assembly in New York on Wednesday, Mrs May will say it is time to step up efforts to tackle extremists’ use of the internet and block access to ideologies which ‘preach hatred, sow division and undermine our common humanity’.
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She will hail the shows of solidarity and resilience shown by communities in Manchester and London following terror attacks this year.
But she will say: ‘Defiance alone is not enough. As prime minister, I have visited too many hospitals and seen too many innocent people murdered in my country.
‘When I think of the hundreds of thousands of victims of terrorism in countries across the world, I think of their friends, their families, their communities, devastated by this evil.
‘And I say enough is enough.’
The Islamic State terror group has developed a more sophisticated use of social media than earlier militants like al-Qaeda, disseminating more than 27,000 items through outlets like Twitter in a five-month period between January and May this year.
Links to material ranging from bomb-making instructions to videos glamorising the group and calls to commit atrocities with cars and knives in Western cities are spread rapidly, with the majority of shares taking place in the first two hours.
Experts believe that by removing links more quickly, access to the material can be dramatically reduced, even if it takes longer to eradicate every trace of it from sites like YouTube.
Some of the world’s biggest tech companies, including Facebook, Microsoft and Twitter, will take part in the event hosted by Mrs May, French president Emmanuel Macron and Italian prime minister Paolo Gentiloni, on the fringe of the General Assembly.
Major advertisers will also be present as they start to put pressure on the internet giants to stop ads being screened alongside unacceptable material.
Mrs May will hail progress made by tech companies since the establishment in June of an industry forum to counter terrorism.
But she will make urge them to go ‘further and faster’ in developing artificial intelligence solutions to automatically reduce the period terror propaganda remains available and eventually prevent it appearing at all.
Britain, France and Italy will come together behind a target of one to two hours to take down terrorist content wherever it appears.
One Downing Street source said the companies ‘have been doing something, but just not enough’.
The source said: ‘These companies have some of the best brains in the world. They should really be focusing that on what matters, which is stopping the spread of terrorism and violence.
‘We want them to break the echo chambers.’
In her address to the UN, Mrs May will say: ‘When terrorists struck London and Manchester this year, the world saw our cities come together in defiance.
‘Our parliament carries on. Ariana Grande came back to Manchester and sang again. London Bridge is bustling with people. Our communities came together at the mosque in north London. And Londoners got back on the Tube.
‘The terrorists did not win, for we will never let anyone destroy our way of life.
‘But defiance alone is not enough. In the last decade hundreds of thousands have been killed by terrorists across the world. This is a truly global tragedy that is increasingly touching the lives of us all.’
Google and YouTube have already announced they are increasing their use of technology to help automatically identify offending videos, while Facebook has said it is looking at automated identification of terrorist material.
Twitter suspended 299,649 accounts between January 1 and June 30 this year, 75% of which were blocked before their first tweet.
Facebook has said publicly that it is looking at developing artificial intelligence to automate the identification of terrorist material.