Brenton Tarrant, from Grafton in NSW, has been charged with murder over the attack in New Zealand that killed 50 people and left another 50 injured and was live-streamed on Facebook.
"Social media companies are international businesses and it's up to the international community to force them to act," Mr Morrison said on Tuesday.
In his letter, the prime minister says it's unacceptable to treat the internet as an ungoverned space.
He argues the global community needs to ensure tech companies meet their moral obligation to serve communities they profit from.
Tarrant, 28, was not on any security watchlist in Australia or New Zealand, despite online profiles linked to him containing material promoting white supremacist views.
New Zealand Prime Minister Jacinda Ardern said her government did all it could to remove the online footage in the wage of the attack but it was up to the digital platforms to make sure it was deleted.
"There are further questions to be answered," Ms Ardern said earlier this week.
Facebook said it took down 1.5 million copies of the footage and authorities were last week left scrambling to stop its spread across the internet on Twitter, Google and elsewhere.
On Monday, Mr Morrison said Australian authorities were watching for the rising threat of far-right extremists following the attacks.
"This is not a new area of activity for our security agencies, they have been monitoring this area for quite a long time," Mr Morrison told an Australia Israel Chamber of Commerce function in Melbourne.
"Sadly, white supremacy in sections of Australia is not new.
"It's a serious issue. It will always get more and more attention."
Mr Morrison met with security agency bosses on Monday afternoon to hear their responses to the NZ attack.
Labor leader Bill Shorten said Australia's police forces needed a common definition of hate crimes so they can be tracked.
"This country needs to be better at recording hate crime ... you can't beat what you can't measure," he told reporters in Perth