Anthony Albanese hailed the parliament's Thursday passage of landmark legislation requiring social media firms to take "reasonable steps" to prevent young teens from having accounts.
The law, which will come into effect after 12 months, gives few details of how it will be enforced, including how sites like Facebook, Instagram and X will verify users' ages.
Musk -- who has been named Donald Trump's government efficiency chief in the incoming US administration -- posted on X last month that the law "seems like a backdoor way to control access to the Internet by all Australians".
"We will talk to anyone," Albanese said when asked if he would discuss the legislation with Musk.
"With regard to Elon Musk, he has an agenda. He's entitled to push that as the owner of X, formerly known as Twitter," Albanese told Australian public broadcaster ABC.
When the interviewer mentioned that Musk was also Trump's "right-hand man", the prime minister replied: "We will engage, we will engage."
Social media firms that fail to comply with the new law face fines of up to Aus$50 million (US$32.5 million) for "systemic breaches".
Musk's platform in October lost a legal bid to avoid a US$417,000 fine levelled by Australia's online watchdog, which has accused X of failing to stamp out harmful posts.
- 'Bullying' -
The government will decide over the next 12 months how to implement the ban, Albanese said, insisting, however, that it would not require people to provide identification.
"The obligation will be on social media companies to do everything they can to make sure that those people under 16 don't have access to social media," the prime minister said.
"We know that social media companies have more information about you and I than some of our friends do," he added.
"We know that they are able to do that, and the obligation will be on them."
Albanese said he was "determined" to implement the legislation.
"I've met parents who have had to bury their children as a result of the impact that social media has had as a result of bullying, and we need to do something about it," he said.
Several social media giants have promised to work with the government on implementing the law.
But they have also criticised the legislation, saying it was "rushed", full of unanswered questions, and did not take into account the views of experts who opposed it.
The UN children's charity UNICEF Australia warned this week that the law was no "silver bullet" against online harm and could push kids into "covert and unregulated" spaces online.