The firms will also be challenged to "develop new technological solutions to prevent such content being uploaded in the first place", as Ms May claims world leadership on the controversy at the United Nations.
The PM will host a meeting with the world's biggest tech firms in NY.
Joining the gathering of world leaders will be the likes of Facebook, Microsoft and Alphabet's Google, who will take part in a meeting aimed at tackling the propagation of extremism through the Internet.
Bosses from Facebook, Microsoft, Google and Twitter will be there.
Earlier in the day, May will use her keynote speech to the U.N. General Assembly to speak of her personal experience of visiting terror victims in hospitals following attacks in London and Manchester this year.
But that's not enough, according to May.
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.
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.
She will warn, however, that terrorists will adapt.
Tips for Canadians caught in Equifax's security hack
Analysts say three Equifax executives, though, may have a hard time explaining their series unusual stock sales. An investigation into the data breach was launched last week by Canada's privacy watchdog.
"Terrorist groups are aware that links to their propaganda are being removed more quickly, and are placing a greater emphasis on disseminating content at speed in order to stay ahead", May plans to tell the event.
The prime minister's spokesperson told journalists they were working with tech companies who were "making progress in the right direction", but there was "significantly more to do". "We're looking forward to helping bring new ideas and technologies to life", said Kent Walker, general counsel at Google.
Twitter alone has suspended almost 300,000 accounts so far this year, with the company revealing 95 per cent of them were detected automatically by artificial intelligence.
"Mistakes will inevitably be made - by removing the wrong content and by missing extremist material", he said in a statement.
The companies a year ago chose to set up a joint database to share unique digital fingerprints they automatically assign to videos or photos of extremist content, known as "hashes", to help each other detect and remove similar content.
The issue will be at will be top of the agenda at the next G7 meeting on October 20.
"These companies have some of the best brains in the world", a Downing Street source said.
Their goal is to persuade these tech giants that stopping terrorists from using their platforms should be a priority and the focus for innovation.
It was reported that once a person shows a bit of interest in such materials, algorithms used by search engines keep directing them to similar content and that it was this "echo chamber" that internet companies need to break.