Media chiefs and the federal opposition are urging Peter Dutton to abandon any legal action against journalists targeted in recent federal police raids.
Two ABC reporters and a News Corp journalist are under police investigation after publishing separate stories based on leaked government information.
The heads of both media organisations have written to the home affairs minister, asking that action against their journalists cease.
Opposition Leader Anthony Albanese has endorsed their demands.
"That's a common sense outcome," Mr Albanese told reporters in Sydney on Thursday.
"These are journalists who are doing their job, and the fact is the idea that they were under investigation was dismissed by the government just weeks ago."
The high-profile police raids have attracted international attention and triggered a fierce debate on press freedom in Australia and abroad
As a consequence, Foreign Minister Marise Payne has been forced to defend her attendance at an international conference on media freedom.
The foreign minister was at the Global Conference for Media Freedom in London on Wednesday with her international counterparts, journalists and civil groups.
Senator Payne denied she was being hypocritical, saying she was in a "no-win" situation.
"I would imagine that if Australia was not represented at a conference like today, then you would say that the government wasn't doing their job by being here," she told reporters.
"So I suspect you would advance a position where a government was in a no-win situation."
Mr Albanese was highly critical of her attendance.
"I do find it quite extraordinary that a government that's presided over these attacks on press freedom has a foreign minister overseas speaking at conferences about press freedom," he said.
"I think that Australia would have more credibility if we get our act together right here, right now."
Meanwhile, a former military lawyer charged with leaking classified documents at the centre of the ABC raids has faced court again in Canberra.
David McBride has agreed to keep journalists out of the courtroom when secret information comes up in his trial.
The 55-year-old will be back before the ACT Supreme Court next week.
In London, the foreign minister told the conference's plenary session that Australia condemned Saudi journalist Jamal Khashoggi's murder at the Saudi consulate in Istanbul last year.
Senator Payne also talked about how she raised the plight of two Reuters journalists jailed in Myanmar with leaders in that country in December.
But she did not mention Australian Federal Police raids on the News Corp journalist Annika Smethurst's home or the ABC headquarters, or their requesting of ABC journalist Dan Oakes' private travel records.
The foreign minister also did not make any mention of the AFP accessing journalists' metadata 58 times in one year.
"While Australia ranks relatively highly on the World Press Freedom Index, we recognise that a sensible balance needs to be reached between protecting our national interest in the face of ever-evolving security challenges and upholding the public's right to know," Senator Payne told the conference session.
She said that was why a parliamentary committee was looking into law enforcement, intelligence and press freedom.
Australian Associated Press