Social media companies such as Facebook and Twitter could face fines if they fail to remove extremist propaganda and terrorist material under proposals agreed by the UK and French governments.
The two countries are to develop plans to create a new legal liability for tech firms which fail to take action against unacceptable content on their platforms.
They will lead also work with internet giants to explore the potential for new tools to identify and remove harmful material automatically.
Speaking ahead of a visit to French President Emmanuel Macron in Paris on Tuesday in the wake of atrocities in Westminster, Manchester and London Bridge, Theresa May said the countries were determined to ensure the internet could not be used as a safe space for terrorists and criminals.
She said: “The counter-terrorism co-operation between British and French intelligence agencies is already strong, but President Macron and I agree that more should be done to tackle the terrorist threat online.
“In the UK we are already working with social media companies to halt the spread of extremist material and poisonous propaganda that is warping young minds.
“And today I can announce that the UK and France will work together to encourage corporations to do more and abide by their social responsibility to step up their efforts to remove harmful content from their networks, including exploring the possibility of creating a new legal liability for tech companies if they fail to remove unacceptable content.
“We are united in our total condemnation of terrorism and our commitment to stamp out this evil.”
Mrs May’s visit comes just days after legislative elections in France which appear to have delivered Mr Macron’s En Marche party an overwhelming dominance in parliament, just as the UK General Election deprived the Prime Minister of her own Commons majority.
The leaders will press tech companies to move forward urgently with the establishment of an industry-led forum to develop shared technical and policy solutions to the problem, as agreed by leaders of the world’s most advanced economies at last month’s G7 summit in Italy.
Home Secretary Amber Rudd and French interior minister Gerard Collomb will meet in the coming days to drive the agenda forward.
Labour MP Yvette Cooper, who chaired the House of Commons Home Affairs Committee in the last parliament, said: “Social media companies like YouTube have been getting away with a dangerous and irresponsible approach to extremism for too long.
“Still today YouTube is showing illegal propaganda videos for banned jihadi and neo-Nazi extremists. They have a disgraceful disregard for the law.
“The cross-party Home Affairs Select Committee called for a system of fines and stronger legislation.
“So if that is what the British and French governments are working on now, that is really welcome.
“They need to make rapid progress, because online radicalisation is a very serious threat, and this problem has been growing for a long time.”
Facebook last week pledged to be a “hostile environment” for terrorists after Mrs May demanded action from internet firms following the London Bridge terror attack.
The social media website said it worked “aggressively” to remove extremist content and notify police of any threats, while Google and Twitter also defended themselves from claims web giants provide a “safe space” for terrorists.
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