Bill Shorten has affirmed Labor’s commitment to follow the recommendations of an independent selection panel in choosing new appointees to the ABC board should they form government, while again calling for Mitch Fifield to be removed from his portfolio.

Justin Milne resigned as ABC chairman last Thursday, amid allegations he compromised the independence of the public broadcaster, just days after Michelle Guthrie was sacked from her position as managing director. The allegations sparked staff protests, a departmental inquiry and prompted renewed scrutiny of the appointment of ABC board directors.

Shorten on Tuesday accused the government of interfering in the public broadcaster and linked the issue with a need for a national integrity commission.

“They interfere with the choice of directors, they cut the funding of the ABC, they appoint their mates and that doesn’t work out, and then they just blame the ABC for everything that is going wrong,” he said.

“This is a failure of governance, it’s a failure of politics, it’s a failure of the government. This is why we should have a national integrity commission. I do not know why [Scott] Morrison is opposing setting up an anti-corruption commission nationally, because I think that would provide reassurance to Australians that the political system is not broken.”

Shorten also committed a future Labor government to following the recommendations of the independent selection panel in choosing new appointees to the broadcaster’s board, as the opposition sought to keep the government’s role in last week’s turmoil in the headlines for another week.

He also repeated his call from Monday to have a bipartisan approach to selecting new permanent appointments, with the ABC currently helmed by both an interim chair and acting managing director.

But he saved his most scathing attack for the communications minister. Last week, Guardian Australia revealed Fifield had either circumvented or ignored the independent panel’s recommendations for the last five appointments he has made to the board.

Fifield has previously said he took the panel’s recommendations on board but followed the process that allows for the government to make the final decision.

“It is a legislative requirement that panel process be gone through,” Fifield told a Senate estimates hearing last year. “Recommendations are made and then it is up to the government to accept some of those recommendations.”

Shorten said that left the blame for last week’s chaos at Fifield’s door.

“That guy has got more lives than a cat – you know, nothing ever sticks to this fella,” he said. “The reality is that he’s the communication minister, where you’ve got the chairman miraculously, telepathically apparently, understanding the wishes of the government and wants to see journalists sacked.”

Shorten also called for the ABC board to be “depoliticised”.

“As for the board, I think the government needs to hang its head in shame,” he said. “You don’t have an independent process and then totally ignore it for every director, and how much did these board directors know what’s going on?

“I think we’ve got to depoliticise board appointments to the ABC.”

The former federal Liberal deputy leader Neil Brown, who was also a previous member of the ABC board selection panel, told Fairfax Media on Tuesday that Fifield was “making a fool of himself” for ignoring the panel’s advice on so many occasions.

Following his resignation, Milne said the ABC’s interests had always been “utmost in my mind” and said there was “absolutely no interference in the independence of the ABC by the government”.