Anthony Albanese is trying to build an international coalition to clamp down on children's access to apps, such as Instagram, TikTok and Snapchat.
He was joined by parents who have campaigned for tougher social media laws at an event for world leaders in New York City.
They included NSW mum Emma Mason, whose daughter Tilly, 15, took her own life after being bullied on social media.
"I'm standing up for her and telling her story so that other children don't endure what she had to," Ms Mason said.
Australia will introduce social media age restrictions on December 10.
"This is a sensible but overdue step to protect young Australians at a critical stage of their development, giving them three more years to build real world connections and online resilience," Mr Albanese said.
Europe is considering introducing similar laws, to bar children under 16 from social media.
But Australia's age restrictions could cause friction with the US, where many major online platforms are based.
The White House has raised concerns about other laws cracking down on tech giants' use of Australian news content.
The issue could be discussed when Mr Albanese sits down with US President Donald Trump in Washington on October 20 after months of back-and-forth to secure a face-to-face meeting.
The Oval Office talks were announced after Mr Albanese briefly met the president at a reception for world leaders on Wednesday.
The pair posed for a selfie, which Mr Albanese posted on social media.
The prime minister described their interaction as a "very warm and engaging chat".
"We look forward to a further discussion in a few weeks' time," he told reporters in New York.
The meeting in October will be significant but potentially risky, given the tongue-lashing other world leaders have received during White House talks, Australian Strategic Policy Institute Senior Fellow Mark Watson said.
"Anything other than abject humiliation would be a success," he told AAP.
Mr Watson, who spent 33 years at the Department of Foreign Affairs and Trade, including a stint in Australia's US embassy, said the prime minister would likely seek reassurances from Mr Trump on the AUKUS nuclear submarine deal.
The US is reviewing the three-country agreement, which includes the UK, to ensure it aligns with Mr Trump's "America First" agenda.
This is the prime minister's last full day in the US. He is due to meet his Sri Lankan counterpart and potentially sit down with Turkey's strongman leader, Recep Tayyip Erdogan.
Earlier, speaking at the UN, Mr Albanese promoted Australia's new goal to reduce greenhouse gas emissions by 62 to 70 per cent on 2005 levels by 2035.
Australians know that extreme weather events are becoming more frequent and intense, the prime minister said, and the next decade would be decisive for action on climate change.
"An essential message that each of us can send to our citizens is this: it is not too late," he said.
"If we act now and move with common purpose, then we can do more than just guard against the very worst."
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