The Online Safety Amendment (Digital Duty of Care) Bill is among a clutch of legislation the government is hoping to pass as parliament resumes sitting from Monday.
The bill will put the onus on social media companies to ensure under-18s aren't exposed to harmful content, such as pornography, bullying and material that glorifies crime.
The Greens are expected to support the laws following the removal of a controversial clause giving the communications minister sweeping discretion.
But the minor party believes the legislation does not go far enough, calling on the government to give people safe legal pathways to get compensation from tech companies if they are harmed by online content.
"These huge tech companies make billions of dollars trapping Australians on their addictive platforms," Greens senator Sarah Hanson-Young said.
"To change their behaviour, they will only respond to one thing: penalties that really hit their bottom line.
"To meaningfully change the behaviour of big tech companies, the digital duty of care laws must include the right for Australians who have been harmed online to be able to take legal action and seek compensation for the damage done."
The plan comes as the government grapples with its approach to an upcoming execution by firing squad in the United States, expected to be live-streamed in December.
The Trump administration plans to show the execution of Fort Hood shooter Nidal Hasan, but there have been calls for it to be blocked in Australia.
The return to parliament comes as multiple polls point to a slide in support for One Nation from recent highs.
The anti-immigration party was behind Labor for primary support in the latest Newspoll and Resolve surveys, while a DemosAU analysis for Capital Brief suggested it was losing momentum in its regional heartland.
The latter data, based on polling of 9740 Australian voters in August and September, suggested Labor would likely win a slender majority in parliament if an election were to be held.
Its central projection was for One Nation to win 24 seats, while the coalition would lose eight from its current tally to sit on 34.
On Tuesday, Prime Minister Anthony Albanese will welcome King Abdullah II of Jordan to Canberra.
Jordan is a key defence partner for Australia and a major player in the Middle East, where war continues to rage.
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