Justin Milne, a wealthy technology entrepreneur and former business associate of Malcolm Turnbull, the former prime minister, resigned after documents showed that he had pushed to have the broadcaster's senior political reporter dismissed because Mr Turnbull "hates" him.
The current crisis began with the unceremonious ouster earlier this week of ABC managing director Michelle Guthrie, reportedly pushed out by Mr Milne due to her poor relations with Canberra and a range of internal managerial missteps.
"My aim, has been to look after the interests of the corporation. Get rid of her", Milne wrote to Guthrie, according to Fairfax Media.
The scandal has damaged the credibility of both the governing coalition and the ABC, which is government-funded but is required by law to operate independently of party politics.
"There was absolutely no interference in the independence of the ABC by the government".
The rhetoric at a smaller gathering in Brisbane was stronger, where a resolution was passed demanding Mr Milne resign.
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The BBC also reported that the cabinet remained fully behind May's Brexit policy in the face of growing calls within her party to change direction.
Meanwhile, the Morrison government has ordered the communications department to investigate the allegations levelled at Milne.
On Thursday, Milne, a former executive at Australian telecom giant Telstra, described the recent reports as a "firestorm" and said he made a decision to quit because he "wanted to provide a release valve" for the network.
In light of the revelations of interference, ABC staff held meetings across the country, with Melbourne staff declaring Milne should stand aside while an independent enquiry takes place.
Australia's conservative government has traditionally been at logger heads with the ABC, which it perceives as being left wing, with the relationship souring further this year following a funding cut.
Mr. Milne, who was appointed by the conservative government past year and is a friend of former Prime Minister Malcolm Turnbull, said he had quit for the good the corporation. On another story about innovation, the ABC issued a minor clarification but otherwise rejected the government's complaints.
Alberici suggested Mr Milne may have a conflict of interest, because he is also chair of a company she has written about regarding corporate tax.
An Essential poll released on September 25 said 54% of those surveyed trusted the ABC, vastly more than said they had faith in the federal parliament (28%) or Australia's political parties (15%).