Media bosses have sought assurances from the Morrison government that reporters caught up in high profile raids would be immune from prosecution.
The Morrison government has refused to guarantee journalists raided by police last month will be immune from prosecution.
Media bosses sought the assurances during a meeting with Attorney-General Christian Porter and Communications Minister Paul Fletcher on Wednesday but were rebuffed.
"We had a constructive discussion ... but we remain frustrated that a month after search warrants were carried out by the Australian Federal Police the fate of our journalists remains unclear," ABC managing director David Anderson said in a statement.
They also have concerns over the government's plan to use the often-secretive parliamentary intelligence and security committee to examine how police and intelligence powers have impacted the media.
"We'll continue to work with them on that, but it would be fair to say our concerns about that forum have not gone away," News Corp's director of corporate affairs Campbell Reid told reporters.
The government favours a short, sharp, targeted inquiry by the Parliamentary Joint Committee on Intelligence and Security.
It would look at when and why journalists and media organisations come under the scrutiny of police and spooks, and critique the thresholds for when police should follow up leaks.
Mr Anderson said media organisations would engage with any processes that sought to address their concerns, but their preference was for "immediate action rather than inquiries".
"We will continue to push for real outcomes that strengthen the Australian public's fundamental right to know," he said.
"We have committed to making further direct submissions both on the fate of our journalists and on the specific areas where freedom of the press has been eroded and we have agreed to meet with the attorney-general and minister for communications again in three months' time."
He said the government should set the tone for a less secret and more open democracy.
The organisations represented at the meeting included the ABC, News Corp, Nine, Free TV, SBS and Seven West Media.
Labor has planned a separate, broader inquiry, via a committee set up for that specific purpose, and is expected to push for it in parliament on Thursday.
"The questions about the public's right to know and media freedom are broader than just national security legislation," opposition home affairs spokeswoman Kristina Keneally told Sky News.
Labor's proposed inquiry would look at disclosure and public reporting of sensitive and classified information.
Whistleblower and public servant protections would also come under scrutiny, along with how the government refers leaks to authorities and the independence of police in dealing with politically sensitive matters.
The Canberra home of News Corp journalist Annika Smethurst was raided last month over the 2018 publication of a leaked proposal to allow the Australian Signals Directorate to spy on Australians.
The following day, the ABC's Sydney headquarters were raided over stories published in 2017 alleging Australian soldiers may have carried out unlawful killings in Afghanistan, based on leaked Defence papers.