Proposed laws across the Tasman would:
• Make it a criminal offence to fail to remove the offending footage as soon as possible after it was reported or it otherwise became known to the company
• Allow the government to declare footage of an incident filmed by a perpetrator and being hosted on a site was "abhorrent violent material". It would be a crime for a social media provider not to quickly remove the material after receiving a notice to do so. There would be escalating penalties the longer it remained on the social media platform.
Further details are pending. It's so far not clear if Australia or NZ will follow the lead of Germany, which designated social media platforms as publishers and threatened them with fines of up to 50 million Euros ($80m) if they failed to act on hate speech.
Morrison has already said he wants to put a multi-country social media crackdown on the agenda for June's G20 meeting.
Here, Prime Minister Jacinda Ardern has said she wants to meet with executives from Facebook, and said she wants social media companies to do more - but details of the meeting or an action plan are still pending.
Attorney-General David Parker raised social media at a Five Eyes meeting last August - but yesterday refused to answer questions.
Speaking at the recent swearing in of Justice Helen Winklemann as Chief Justice before the mosque shootings, Park posed the question, "Where does the limit lie between freedom of speech and harmful fake news or hateful propaganda?
"What duties are owed by those who profit from social media platforms to society, private citizens, or to the public institutions which democracy relies on?"
With reporting by The Conversation.