The ABC board has passed a unanimous vote of confidence in the broadcaster's managing director David Anderson after union members called on Mr Anderson to take immediate action to win back the confidence of staff.

Speaking on behalf of the ABC board, chair Ita Buttrose said it was "abhorrent and incorrect that people would suggest that (Mr Anderson) has shown a lack of support for independent journalism and journalists." 

"David Anderson has always been a strong supporter of the independence of the ABC and its journalists," Ms Buttrose said in a statement. "He has encouraged them to report without fear or favour and has never weakly surrendered to criticism as some critics have alleged.

"The ABC regularly receives, and responds to, complaints from individuals or organisations and the assumption that either the managing director as editor-in-chief or I would be influenced by any sort of lobbying pressure is quite simply wrong.

"The board, including the managing director, recognise that this is a very difficult environment for our staff with many societal issues that threaten to divide us. We will continue to prioritise actions that support our staff, ensure our journalistic independence, and protect the trust that Australians place in the ABC."

ABC members of the Media, Entertainments and Arts Alliance (MEAA) passed a vote of no confidence in Mr Anderson on Monday.

The vote was passed at a national online meeting attended by more than 200 ABC employees who are union members.

The board met on Tuesday to discuss an unlawful termination claim brought against the ABC by journalist and former presenter Antoinette Lattouf.

Her Fair Work Commission submission claims the ABC told her she breached the organisation's social media policy for posting content from Human Rights Watch about the war in Gaza on her personal Instagram account.

The claim also alleges Ms Lattouf, who is of Lebanese heritage, was dismissed based on her race.

The ABC has rejected the claims and lodged its defence.