The outgoing chairman said his decision was driven by a need to protect the broadcaster's reputation and denied he had ever been pressured to sack reporters by members of the Turnbull or Morrison governments.
"Nobody from the government has ever rung me and told me what to do in relation to the ABC. Nobody ever told me to hire anybody, fire anybody or anything else. They absolutely didn't," he said.
"I know that's the sort of narrative that's been running in the papers but that absolutely never happened."
Mr Milne also said he never demanded anyone be sacked because the government didn't like their reporting, but maintains he was entitled to intervene in editorial issues.
"When there is an issue of editorial independence and accuracy it's appropriate for the chair to be involved - it's the chair's job.
"[But] I have never sent an email to Michelle Guthrie or anybody else, which says you must sack Emma Alberici or Andrew Probyn or anybody else."
Prime minister Scott Morrison tweeted that the chairman and the board made the "right call" and said it was time for the ABC to "resume normal transmission".
Earlier, the prime minister described allegations Mr Milne demanded the sackings of senior journalists as “very concerning”, but denied the chairman's comments were a consequence of political pressure from the Coalition.
“They're pretty serious allegations I've got to say. And on the face of it they’re very concerning,” Mr Morrison said.
The Labor opposition went further, saying it no longer had “confidence” in his leadership and describing his position as “untenable”.
Communications department to investigate within 'days'
The prime minister said he would not “prejudge” a recently announced Communications department inquiry into alleged political interference.
The communications minister said he expected the inquiry to take "days, not weeks".
Speaking at a Queensland strawberry farm hours before Mr Milne resigned, Mr Morrison said the facts of the matter needed to be determined "before anybody races off on anything here".
Minutes after Scott Morrison spoke, Labor’s shadow communications spokesperson Michelle Rowland declared the opposition believed the chairman should step down.
Ms Rowland said she had spoken with Mr Milne and had not been “satisfied” by his answers on questions over whether he was pressured by the government.
“If Mr Milne is incapable of answering some of the very serious questions that go to his role of being independent and acting with integrity in this role, certainly his position as chairman should be considered untenable,” she said.
Coalition denies political pressure
Senior members of the Coalition government have denied applying political pressure to the ABC leadership.
Communications minister Mitch Fifield said he had never done so, and was “not aware” of any other members of the government doing so either.
He said he had raised factual “inaccuracies” in ABC reporting, as with other commercial media, but said those complaints had never extended to pressure to fire a journalist.
“I have always respected the independence of the ABC. Like most members of parliament, I have, on occasion, raised with the ABC issues of facts in reporting, as indeed I've done with commercial media organisations,” Mr Fifield told reporters in Melbourne.
“But, at no stage, and in no way, shape or form, have I ever sought to involve myself in staffing matters in the ABC, nor, for that matter, am I aware of any member of the Government who has sought to do so.”
The minister said he had spoken to Mr Milne to inform him the Communications department would investigate the matter. Mr Milne indicated he "would be cooperating", Mr Fifield said.
The ABC's acting managing director David Anderson emailed staff on Thursday afternoon in a bid to reassure them the organisation's independence would "never be compromised".
"I understand the upset and disquiet caused to many of our people through these events and want to offer you my support," Mr Anderson wrote in the email seen by SBS News.
Turnbull: I never asked for reporters to be sacked
The communications minister's comments came after a similar denial from former prime minister Malcolm Turnbull.
Mr Turnbull denied asking ABC chairman Justin Milne, his former business associate, to put pressure on the ABC's managing director to sack some of the broadcaster's most senior journalists, including its politics and economic correspondents.
Fairfax Media reports allege that while still prime minister, Mr Turnbull called Mr Milne to complain about a report on the government's company tax cuts produced by chief economics correspondent Emma Alberici, which he claimed was full of inaccuracies.
An explosive email has revealed Mr Milne told his former ABC managing director Michelle Guthrie to fire Ms Alberici in May.
Mr Milne was also said to have ordered Ms Guthrie to fire the broadcaster's political editor Andrew Probyn, telling her "you just have to shoot him", because Mr Turnbull hated him.
Speaking in New York, Mr Turnbull defended complaining about ABC "inaccuracies" but strongly denied asking for any reporters to be sacked.
"That is not right. The bottom line is I have never called for anybody to be fired," Mr Turnbull told News Corp Australia.
"My concern has been on the accuracy and impartiality of news reporting.
"Accuracy is critically important and I have to say... [the ABC] has failed in that regard in a number of examples in recent times."
Labor, Greens want additional Senate inquiry
The Greens and Labor are seeking a Senate inquiry into allegations of political pressure on the ABC, saying the internal departmental probe could not be relied upon to uncover the full story.
They will likely have the numbers to establish an Upper House inquiry with the support of some crossbenchers.
The ABC's news director Gaven Morris published an article on the ABC's website to "reassure" its audience the broadcaster was independent.
"Today, the Australian public has asked to be reassured that the ABC's independence is protected," Mr Morris wrote.
"It has been and it always will be. Australia's public broadcaster acts only in the interests of the Australian public and our independence is our most precious asset."
Source: AAP/The Walkley Foundation
Mr Turnbull said the question of whether Mr Milne should resign was "a matter for him".
"I want to be very clear, I have not complained and do not complain about left/right bias," Mr Turnbull said.
"My concern has been purely about the accuracy and impartiality of news and current affairs reporting on the ABC."