A 17-minute video of the March 15 rampage that claimed the lives of 50 people was widely available online and experts said it was easily retrievable several hours after the attack.
"Big social media companies have a responsibility to take every possible action to ensure their technology products are not exploited by murderous terrorists," Prime Minister Scott Morrison said in a statement.
Morrison, who met with a number of tech firms Tuesday -- including Facebook, Twitter and Google -- said Australia would encourage other G20 nations to hold social media firms to account.
Attorney-General Christian Porter said the new laws would make it a criminal offence for platforms not to "expeditiously" take down "abhorrent violent material" like terror attacks, murder or rape.
Executives could face up to three years in prison for failing to do so, he added, while social media platforms -- whose annual revenues can stretch into the tens of billions -- would face fines of up to ten percent of their annual turnover.
Google, Facebook face hefty fines if Australian privacy laws breached
"Mainstream media that broadcast such material would be putting their licence at risk and there is no reason why social media platforms should be treated any differently," Porter said.
The government was so far "underwhelmed" by the response from tech giants at their Tuesday meeting with Morrison, communications minister Mitch Fifield told reporters Saturday.
Facebook said on Tuesday it was "committed to working with leaders and communities" around the world to "help counter hate speech and the threat of terrorism". The company declined to comment further on Saturday.
Cyber-security expert Nigel Phair cast doubt over the likelihood the proposed Australian laws could impose jail time.
Extradition is complicated and reserved for "serious criminal matters", the University of New South Wales academic and former federal police officer told AFP, while Australian-based executives were not company "decision makers".
"Jail is for violent offenders not a marketing representatives in Australia of an American social media company," he added.
But Phair said social media firms can also do more than they pledged at the Tuesday meeting.
"They didn't read the tea leaves then, it'll be different how they read the tea leaves now," he said.