Federal Labor says the Coalition must stand up for press freedom, while its leader said there is only so much it can do from opposition.
Labor leader Anthony Albanese says his party will examine a breadth of suggestions for protecting press freedom, but has stressed he is limited in how he can grapple with the issue from opposition.
Mr Albanese says Prime Minister Scott Morrison's government must take the lead on ensuring the freedom of the press, following Australian Federal Police raids on two media outlets.
"We'll examine all of those issues, but bear in mind that I'm here as the Labor leader, not as the leader of the government," Mr Albanese told reporters in Perth on Sunday.
"The government needs to actually respond to these issues.
"We're not in a position to determine legislation. The government has an absolute majority in the House of Representatives."
Mr Morrison has insisted the government is committed to press freedom as well as ensuring that no one is above the law.
The AFP last week raided ABC's Sydney headquarters and the Canberra home of News Corp journalist Annika Smethurst, over stories that were the result of leaked information.
The ABC was raided over 2017 stories on allegations Australian soldiers may have carried out unlawful killings in Afghanistan, based on leaked Defence papers.
The warrant executed on Ms Smethurst's home was over the 2018 publication of a leaked plan to allow the Australian Signals Directorate to spy on Australians.
Labor has also been keen to highlight that the AFP's two raids preceded it dropping an investigation into the leaking of details of a classified briefing about the so-called Medevac Bill, which changed the process for asylum-seeker medical transfers.
Centre Alliance Senator Rex Patrick is pushing for Australia to protect freedom of expression, including press freedom, in its constitution.
He argues the step, which would require a referendum, is necessary to deal with inconsistencies between existing laws.
"Rather than perhaps go back and adjust every single one of them, if we had, as we should have, a provision in our constitution that protects freedom of the press, it would change the lens through which those laws were interpreted and indeed, may make some of them completely invalid," he told Sky News.