It comes after shootings at two Christchurch mosques in March, which left 51 people dead, were live-streamed on the social media site by the lone gunman.
Ahead of an online extremism summit in Paris attended by world leaders, Facebook said it was introducing a “one-strike” policy for use of Facebook Live, restricting access for people who have faced disciplinary action for breaking its most serious rules anywhere on its site.
First-time offenders will be suspended from using Live for set periods of time, Facebook said.
It is also broadening the range of offences that will qualify for one-strike suspensions.
Prime Minister Theresa May, French President Emmanuel Macron and Canadian Prime Minister Justin Trudeau will be among the leaders attending the Paris summit.
Mrs May will come face to face with her former coalition government colleague Sir Nick Clegg, now an executive of Facebook.
The summit will also be attended European Commission president Jean-Claude Juncker, Irish PM Leo Varadkar and bosses of Twitter, Google, Microsoft and Wikipedia.
The aim is to step up international efforts to stop social media being used to organise and promote terrorism. A joint pledge, the “Christchurch Call To Action”, to eliminate terrorist and violent extremist content online will be signed.
Ahead of the summit, the prime minister said: “The sickening attacks on Muslim worshippers in Christchurch shocked the world.
“That 1.5 million copies of the video had to be removed by Facebook – and could still be found on YouTube for as long as eight hours after it was first posted – is a stark reminder that we need to do more both to remove this content, and stop it going online in the first place.
“While we have seen significant progress on this issue since the terror attacks on the UK in 2017, the live-streaming of these attacks exposed gaps in our response and the need to keep pace with rapidly changing technological developments.
“My message to governments and internet companies in Paris will be that we must work together and harness our combined technical abilities to stop any sharing of hateful content of this kind.”
In her intervention at the summit the prime minister is expected to raise concerns about the growing threat posed by the Far Right, and call for greater progress to develop technical solutions and better collaboration between online platforms.
On the need for international action she is expected to say: “I want the internet to be a safe place for all our citizens.
“That’s why we announced plans for new legislation in the UK – creating a legal duty of care on internet companies to keep users safe from harm. This will be backed up an independent regulator with the power to enforce its decisions.
“We are the first country to put forward such a comprehensive approach, but it isn’t enough for us to act alone.
“The internet is global and online threats have no borders. Companies should be held to consistent international standards, so their customers enjoy the same level of protection wherever they live.”
The event comes as new analysis from the Home Office reveals a white nationalist and neo-Nazi discussion forum – which is not being named for operational reasons – has seen more than 12 million posts in response to almost one million individual threads, and amassed more than 800,000 visits in just one month, with 10% appearing to originate from the UK.
UK government analysis has also highlighted how a variety of different platforms and a wide range of anti-establishment themes are being used to lure in a broader audience, and expose them to Far Right material, further underlining the need for enhanced co-operation to keep pace with emerging threats and deal with extremist content before it reaches illegal terrorist thresholds.
On the need to tackle the changing use of the internet by the Far Right, the prime minister is expected to tell the summit: “In 2017 – in the wake of five appalling attacks in the UK – I called for a much greater co-ordinated global response to fight back against Daesh propaganda online.
“Many of the companies here today responded – and, in part thanks to the action you took, last year Daesh propaganda was at its lowest levels online since 2015.
“That shows us what is possible. Our work here must continue in order to keep pace with the threat. But we also need to confront the rise of the Far Right online.”