Labor may draft a series of changes to laws governing the ABC after Bill Shorten accused the broadcaster of a "failure of governance" and claimed some directors only sit on the board because they are "mates" of the government.

The Opposition Leader stopped short of calling for the seven-member board to resign, but said they had serious questions to answer over the botched sacking of managing director Michelle Guthrie and resignation of chairman Justin Milne.

Mr Milne quit last Thursday after it emerged he wanted two journalists to be fired because the government did not like them.

Ms Guthrie gave the board detailed evidence of Mr Milne's demands but the directors - who have a legal obligation to protect the ABC from interference - only moved against the chairman after the claims became public.