ABC chairman Justin Milne is under further pressure to resign after allegations he ordered former managing director Michelle Guthrie to fire political journalist Andrew Probyn by telling her to "shoot him".
The revelation comes as former prime minister Malcolm Turnbull denied demanding Ms Guthrie sack chief economics correspondent Emma Alberici over supposed impartiality.
An email has shown Mr Milne told Ms Guthrie to fire Ms Alberici in May.
"They [the government] hate her," he wrote in an email to Ms Guthrie obtained by Fairfax Media.
Mr Milne is also said to have ordered Ms Guthrie sack the broadcaster's political editor Mr Probyn, telling her "you just have to shoot him" because Mr Turnbull hated the journalist.
But speaking in New York where he was due to address a United Nations general assembly side event, Mr Turnbull denied he had asked for specific ABC reporters to be axed.
"That is not right. The bottom line is I have never called for anybody to be fired," he said, according to News Corp Australia.
"My concern has been on the accuracy and impartiality of news reporting.
"Accuracy is critically important and I have to say... it (the ABC) has failed in that regard in a number of examples in recent times".
Communications Minister Mitch Fifield has announced his department secretary will run an inquiry into the matter and report as soon as possible.
"It is important for the community to have confidence in the independence of the ABC," he said in a statement.
But Labor and the Greens are pushing for a Senate inquiry into Mr Milne's conduct.
Labor's communication spokeswoman Michelle Rowland says she has now spoken to the ABC chair about revelations he told Ms Guthrie to fire Ms Alberici, but was left with "more questions than answers".
"I do not believe that after discussing the allegations in Fairfax, the explanation he gave was satisfactory," she told the ABC on Wednesday.
"I had a sense there was more information that I needed to know."
Labor and the Greens will attempt to trigger the Senate inquiry before federal parliament resumes in mid-October.
ABC executives will appear before a Senate estimates committee on October 22 and 23, with both sides of politics wanting to know more about why the board sacked Ms Guthrie.
The broadcaster's staff on Wednesday unanimously voted for Mr Milne to step down while the departmental investigation takes place, but the board has confidence in him to continue in his job.
Former ABC managing director David Hill says Mr Milne "has no choice" but to step down given the circumstances.
Mr Milne has released a statement to say he won’t be commenting on the allegations at this stage.
Australian Associated Press