He calls on G20 leaders to "ensure that there are clear consequences, not only for those who carry out such horrific acts, but for those who facilitate them".
In what is being seen as a clear reference to Facebook, Twitter and Google-owned YouTube, Morrison said tech giants should be compelled to act more swiftly in "removing of content by actors who encourage, normalise, recruit, facilitate or commit terrorist and violent activities".
"It is unacceptable to treat the internet as an ungoverned space," he wrote.
"It is imperative that the global community works together to ensure that technology firms meet their moral obligation to protect the communities which they serve and from which they profit.
"The notion of the law applying equally online as it does offline was an underlying principle. In 2018, G20 leaders restated their commitment to full implementation of the Hamburg Statement."
The 2016 Hamburg statement was used by Australia as the rationale for legislation compelling tech companies to work more closely with security agencies and force the breaking of encryption - although some commentators, including the Herald's Juha Saarinen, questioned its practicality, and warned about privacy ramifications and unintended commercial consequences.
New Zealand Prime Minister Jacinda Ardern has said she wants social media platforms to do more to block content and has said she wants to meet with Facebook - the service used by alleged shooter Brenton Tarrant for a 17-minute livestream of the mosque massacres.
Facebook, YouTube and Twitter have so far been energetic in their efforts to block copies of the Christchurch video - or, at least, unedited copies - but silent on the question of whether they will change their livestreaming policies.
