Proposed digital duty of care laws are among a number of bills the government is hoping to pass with the resumption of parliament on Monday.
The legislation 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.
It will also include a "my feed, my way" measure to allow all social media users to opt out of algorithm-driven feeds.
The laws have been amended to remove sweeping powers that would allow the communications minister to decide what constituted harmful content - a key sticking point for some critics.
But opposition communications spokeswoman Sarah Henderson said the plan was still "a blank check for political censorship" and "a dog's breakfast".
"This is an attack on free speech, full and centre," she told News24.
"This (amendment) doesn't improve the bill whatsoever. The bill is fatally flawed and it must be scrapped."
The Greens broadly support the legislation, but they believe it does not go far enough.
The minor party, which holds the balance of power in the Senate, called on the government to give people safe legal pathways to get compensation from tech companies if they were harmed by online content.
"Australians say that if we're getting mucked around by one of these platforms, they should be able to take them on and sue them and fix the harm," leader David Shoebridge said.
"We should have legislation that is empowering Australians."
Communications Minister Anika Wells called for her counterparts to put politics aside and pass the bill, which she said parents had spent years calling for.
Primary school students who were surveyed also wanted crackdowns, she said.
"If a few hundred primary school students can work it out, the adults in this place can too," Ms Wells told Question Time.
Independent MPs Monique Ryan and Zali Steggall confirmed they supported the bill.
"It is essential that we put guardrails around the online environment to make sure there's a safe space," Ms Steggall told AAP.
"It's long overdue and desperately needed."
The return to parliament comes as multiple polls point to a slide in support for One Nation from recent highs, while Labor was still poised to retain government.
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.
