Labor is hoping to garner multi-party support for the contentious social media changes, which have been overshadowed in recent days by simmering feuds centred on One Nation's Pauline Hanson.
Under the proposed laws, tech companies could face fines of more than $100 million for failing to identify and prevent potentially harmful content being shown to users younger than 18.
The banned content includes material encouraging disordered eating, promoting misogyny or online bullying.
While Labor does not plan to legislate the reforms before the end of the year, it is seeking feedback and suggestions for the bill in the hope of achieving broad support.
Opposition Leader Angus Taylor said the drafting of the digital duty of care legislation was a blank cheque on political censorship due to ministerial discretion to define harmful content.
"This is the Big Brother bill, frankly ... they should put forward an alternative. But right now, that's what we're seeing, and we can't support that," he told reporters on Monday.
Communications Minister Anika Wells said she was willing to alter the proposed legislation to ensure it passed.
"I would be prepared to work with the coalition on the wording to make that work that meets the urgency requirement of the intent of that measure," she told the ABC's Insiders program on Sunday.
Liberal senator Sarah Henderson said the draft laws were a "backdoor way" to reintroduce Labor's failed disinformation and misinformation bill.
"This is abhorrent legislation ... we are going to fight it every step of the way," she told News24.
The proposed laws include measures to force social media companies to offer users the option of algorithm-free feeds that show them posts from friends and other accounts they follow.
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