The 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 also 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 coalition labelled the bill political censorship, while newly-elected Greens leader David Shoebridge has drawn a hard line against granting ministerial discretion to proscribe additional harms.
Labor confirmed on Sunday the minister's discretion had been removed and only parliament would be able to add banned content to the legislation.
The government is still hopeful it can win the support of the coalition, but the Greens are unlikely to put up resistance now their main obstacle has been cleared.
While they would not guarantee support until seeing the final legislation, the party was very keen to get the bill passed, a Greens source told AAP while speaking on the condition of anonymity.
The government will also introduce legislation to impose a 30 per cent minimum tax on discretionary trusts, promised in the May budget.
Labor frontbencher Tony Burke said the number of tax-advantaged trusts had doubled to 800,000 over the past 20 years, putting ordinary taxpayers at a disadvantage.
"Where something is set up for the purposes of avoiding the tax that every other Australian taxpayer pays, you can understand why the government's been doing a whole lot of work to make sure that the system is fair," he told News24.
But it comes at a time when the small business sector, which will be severely impacted by the changes, is already at loggerheads with the government over a ban on card surcharges and the scrapping of a generous capital gains tax deduction.
The opposition's Tim Wilson called on Treasurer Jim Chalmers to abandon the trust changes, which risked further "knee-capping" small businesses.
"Small and family businesses have already spent four months paying for legal, financial and valuation advice, and been told restructure costs could hit $50,000," Mr Wilson said.
A Treasury spokesperson said the government had been consulting on the changes and the laws would include options to limit or completely eliminate restructuring costs.
Meanwhile, Prime Minister Anthony Albanese will welcome the King of Jordan, Abdullah II, to Canberra.
Jordan is a key defence partner for Australia and a major player in the Middle East, where war continues to rage.
