Mr Turnbull said he agreed with Ms May's comments after the London terror attacks that "we cannot allow this ideology the safe space it needs to breed. Yet that is precisely what the internet, and the big companies that provide internet-based services, provide."

Mr Turnbull said Ms May had "put her finger on a very important point, that there is too much tolerance of extremist material on social media and that, ultimately, requires co-operation from the big social media platforms, in particular, Facebook and Twitter".

He added that authorities should be given access to private communications, such as encrypted messages.

Facebook and Google on Monday both detailed the extensive and costly approaches they have taken to remove extremist content online, prevent its spread, and pass relevant information to authorities. Twitter declined to comment.

Facebook director of policy Simon Milner said the company wanted its users to feel safe and does not allow terrorists to establish groups on its platform or share extremist material.

"We want Facebook to be a hostile environment for terrorists," Mr Milner said.

"Using a combination of technology and human review, we work aggressively to remove terrorist content from our platform as soon as we become aware of it - and if we become aware of an emergency involving imminent harm to someone's safety, we notify law enforcement."

Google - which owns YouTube, the site where the London terrorists reportedly accessed videos to plan their attack - said hundreds of millions of dollars was spent on removing content which violated its strict guidelines, including extremist material.

"We have clear policies against inciting violence and we remove content that is illegal or that breaks our rules when we're made aware of it," a spokesman said.

Experts have previously said encrypted messaging and the dark web were more frequently used than social media to connect terrorists and plan atrocities.

Photo: Andrew Meares

ASIO director-general Duncan Lewis, above, in evidence given less than a fortnight ago to a Senate estimates hearing, referred to encrypted messaging - but made no mention of social media or tech companies - when discussing emerging terror threats.

Mr Lewis, appearing during a hearing on May 25 - only days after the Manchester terrorist attack - said that "rapid technological change" continued to provide extremists with "new tools to conceal their activities from security and law enforcement agencies", though appeared to mostly be concerned with encryption, not social media.

"I note the widespread use of encrypted communications by our counter-terrorism targets, which remains a particular area of concern," he said.

Fairfax Media understands that federal and state authorities are largely complimentary about the assistance provided to them by social media companies, but are loathe to discuss the extent of those arrangements.

Former counter-radicalisation academic and now Labor MP Anne Aly said, "successive governments have battled with the influence of social media in fostering radicalism for a long time".

They had discovered that the more the internet was scrutinised and wiped off radical propaganda, the more these discussions were driven underground to the "dark web".

Cyber security experts were not convinced that giving governments "back door" access to people's encrypted messages was necessary, and warned it could be dangerous.

"Once you get into the back doors to these products it's a slippery slope," said Nigel Phair, director of the Centre for Internet Safety at the University of Canberra, and formerly with the AFP.

Professor Phair agreed with Mr Turnbull that the big social media companies should "be doing more, a lot more" to curate their platforms and keep a watch on suspicious activity.