According to ABC News Australia, the new laws would require social media companies to collect the details of all users, and allow courts to force the social media firms to hand over the identities of users to aid defamation cases.
"Companies would be required to create a complaints process for people who feel they have been defamed online. The laws would allow courts to force companies to handover the identities of users if people wanted to pursue legal action," the report said on Sunday.
The legislation will be released in draft form this week, and is expected to be introduced in Parliament early next year.
"The rules that exist in the real world must exist in the digital and online world. The online world shouldn't be a wild west, where bots and bigots and trolls and others can anonymously go around and harm people and hurt people," Morrison was quoted as saying in the report.
Under the new law, if the user is unwilling to take down the content, or the complainant wants to take further action, the company asks a user for their consent to release their personal details.
"If the user does not consent to their details being released, a court order can be made requiring the company to release them -- allowing the complainant to pursue defamation action," the report noted.
"We will be looking for test cases that can reinforce these laws. So if the digital companies or others think they're only just going to have to be dealing with perhaps someone of little means seeking to pursue this, then we will look for those cases," said Morrison.
"We will back them in the courts and we will take them on."
Both Twitter and Facebook were yet to comment on the draft laws.
The proposed legislation is part of a larger effort to overhaul Australia's defamation laws.