Anthony Albanese met with parents who advocated for the digital age restrictions and is moving to strengthen existing rules to address widespread noncompliance with the under-16 age limit.
Legislation was introduced into parliament on Monday to double the fines for ban breaches and bolster the online watchdog's powers to investigate social media platforms.
Mr Albanese said the changes would help address the number of children still on social media, which was still too high, but warned the overhaul would not be set-and-forget over the coming years.
"We said when we did this legislation that it wouldn't be perfect," he told reporters on Monday.
"With nudify apps, with algorithms, and with all of these changes that occur with new technologies ... whoever is in government will have to be vigilant and prepared to make changes, and continue to keep on top of this issue."
Mr Albanese spoke with Wayne Holdsworth and Mia Bannister, who both lost children to suicide after harmful experiences online.
Mr Holdsworth, whose son Mac died at 17 after being sexually extorted over the internet, said the age limit would get "better and better" over time.
"It will be a moving feast," he told reporters at a media conference alongside Mr Albanese.
"Along with the legislation, the sanctions - which are excellent - and education, we will defeat the tech giants," said Mr Holdsworth, who is now an advocate against sexual extortion and suicide.
Communications Minister Anika Wells said the tougher laws would grant the eSafety commissioner similar powers to a police investigation, allowing it to demand access to meeting minutes, emails, and communications with third-party providers.
Pressed on why the commissioner was yet to take legal action against any social media platforms despite widespread evidence of the ban being flouted, Ms Wells said the watchdog needed to be a "model litigant" and had to present sufficient evidence to succeed in court.
The opposition says the government's changes are evidence the original plan was rushed and poorly designed.
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