The way the ABC board is appointed won't change despite pleas from Labor to be involved in the process.

The independence of the public broadcaster's board has come under fire after managing director Michelle Guthrie was sacked and chairman Justin Milne forced to resign last week.

Opposition Leader Bill Shorten has written to Prime Minister Scott Morrison calling for a meeting to discuss reforms aimed at restoring confidence in the ABC's independence.

He wants Labor to be consulted on future appointments to the organisation's board, including the next chair.

But the prime minister flatly rejected the idea, saying the government would remain in charge of board appointments.

"I'm sure if they have suggestions they'll make them, but the government runs that process," Mr Morrison told reporters in Perth on Monday.

The ABC has endured a torrid seven days in which Mr Milne sacked Ms Guthrie, before he was forced out.

Mr Milne, a decades-long friend and former business associate of Malcolm Turnbull, quit over allegations he demanded several journalists be sacked to appease the coalition government.

As the dust settles on the crisis, Mr Morrison is urging the taxpayer-funded institution to "get back to work" and "stop talking about themselves".

"The ABC is a very important institution, but frankly, there are a lot of other issues out there that I think are really burning through kitchen tables as topics of conversation than that one," he said.

The accusations levelled at Mr Milne raised concerns about political interference and cast a dark cloud over remaining ABC board members.

Mr Shorten said the coalition government had failed to follow the independent nominations panel process for appointments to the board, which can have up to seven members.

"There should be no partisanship in the appointment of ABC board members, particularly given the proximity to the next federal election," he wrote.

"The ABC does not belong to any political party, it belongs to all Australians."

Mr Shorten said Communications Minister Mitch Fifield had rejected the panel's recommendations or bypassed it entirely several times.

Independent senator Tim Storer wants candidates for positions on the ABC board subjected to US-style confirmation hearings to stamp out political interference.

He wants the independent panel to publish its recommendations and the government to publicly explain its reasoning for any rejections.

If the major parties disagree on an appointment, the nominee would be subjected to a public Senate committee inquiry.