Prime Minister Scott Morrison has demanded the ABC "get back to work" after a leadership crisis at the national broadcaster claimed the scalps of its chairman and managing director.

Mr Morrison has fended off questions about the potential folly of political appointments to the ABC board by arguing it is up to the board to ensure the organisation is well run after a "pretty ordinary" week.

"I think the ABC needs to stop talking about itself and get back to work," he said on Sunday.

Former ABC chairman Justin Milne, a friend and business associate of Malcolm Turnbull, was forced to resign after it was revealed he demanded several journalists be sacked to appease the federal government.

Mr Morrison said he didn't know what was in Mr Milne's mind at the time, but he expected the ABC board under acting chairwoman Kirstin Ferguson to do better.

"Dr Ferguson needs to get on and settle the ship down to make sure they get back to doing what they should be doing in an independent and an unbiased way, to get the facts right, and to ensure they perform the duties the Australian people pay them to do," he said.

"I expect the ABC board to do better. And if they don't, well, they can expect a bit more attention from me."

Shadow Treasurer Chris Bowen said the "extraordinary" interventions of the former ABC chairman exposed a poor culture between the government and its appointments to the public broadcaster's board.

"We do need a parliamentary inquiry to get to the bottom of exactly what interference occurred, what the board knew and when they knew it," Mr Bowen told Sky News.

"It is just unquestionably black and white, open and shut wrong on behalf of the the chairman, and that culture appears to have been allowed to continue under the Liberal government."