Under a long-awaited digital duty of care bill, social media companies would have to identify and mitigate harmful content for users younger than 18.
This would include content encouraging disordered eating, pornography, harmful ideas about women, bullying and life-endangering stunts.
For adult users, illegal content would need to be monitored and quickly removed, along with posts that promoted terrorism, child exploitation and sexual violence.
The communications minister would be given a high level of discretion to determine if content should be removed, which Opposition Leader Angus Taylor warned would be used to stifle free speech and the work of journalists.
The coalition claims were a "straw man argument about political censorship", Communications Minister Anika Wells said in Question Time.
She said experts, parents who had lost children to suicide related to online content, and even coalition members, had demanded social media safeguards.
"The opposition had the opportunity to improve our social media minimum age laws,'' she said.
"The opposition have chosen instead to fling their arms around One Nation and the platforms. They should be ashamed of themselves.
"I ask the coalition to reflect just what they're opposing in the interests of their own internals."
The coalition held a party room meeting on Thursday after it was divided on the government's bill, deciding it would not support the legislation.
The social media reforms will need minor party support to pass.
Mr Taylor said the opposition was concerned about the harm social media caused to children, particularly in instances where people had died by suicide as a result of online content.
"We are always willing to work with the government to protect kids against serious harm," he said.
"What we don't support is a political censorship bill, and sadly, that's what we have in front of us."
Opposition communications spokesperson Sarah Henderson said the draft legislation, originally intended to be announced later in September, was "ham-fisted", rushed and gave sweeping powers to the minister.
Laws to strengthen the under-16s social media ban passed the Senate on Thursday morning.
They allow the eSafety commissioner, currently Julie Inman Grant, to compel access to information for investigating social media use by children.
The maximum fine for company non-compliance will double to more than $100 million.
To date, no companies have been penalised for non-compliance.
The Greens backed the bill, although they raised concerns about the maximum fine being too lax, but the coalition did not.
Mr Taylor said the bill gave "unfettered powers" to the commissioner and communications minister, which would lead to further censorship.
Separately, the government has announced social media users would be able to decide if they wanted to keep algorithms or have a linear feed that prioritised their friends' posts.
Instagram's chief executive Adam Mosseri told reporters on Thursday an algorithm-free world would mean users were bombarded with brand content and would likely spend longer on the app.
"What ends up happening is the best way to get more reach is just to post more often and those who can afford to post the most often do and then therefore get the most reach," he said, according to The Guardian.
Meta, the parent company of Instagram, has been contacted for comment.
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