The Australian Shareholders Association was not swayed by Richard Goyder's evidence to a Senate committee that he retained the backing of the embattled airline's biggest owners and insisted it needs new executives.
"This inability to read the room when government, the media, the business community, investors and the public are calling for change, is concerning, and it will hamper any efforts by Qantas to revive its flagging reputation," the association's CEO Rachel Waterhouse said in a statement.
"It is clear from our members that he does not have the support of the retail investors who own 10 per cent of the company."
Appearing at the Senate committee hearing on bilateral air service agreements on Wednesday, Mr Goyder insisted he had the backing of 14 of the airline's 20 biggest shareholders.
The committee's inquiry is probing the government's decision to deny Qatar Airways extra flights into Australia, with Mr Goyder and Qantas CEO Vanessa Hudson quizzed on what involvement the airline had in that call.
It comes after a series of blows to Qantas' reputation including a High Court ruling the carrier had illegally sacked almost 1700 workers during the COVID-19 pandemic, and the consumer watchdog launching Federal Court action alleging it sold customers tickets on flights it had already cancelled.
The Australian and International Pilots Association on Thursday announced pilots at a Qantas subsidiary in Western Australia would strike for a full day next week amid enterprise agreement negotiations.
The pilots association declined to comment on Mr Goyder's evidence, outside of stating it had done nothing to change their belief his position was no longer tenable.
Also on Thursday, coalition senators announced former CEO Alan Joyce will be summoned to appear at the inquiry upon his return to Australia, and even threatened to try and jail him if he fails to comply.
Earlier this month Qantas announced Mr Joyce was leaving the company, two months earlier than expected, to "help the company accelerate its renewal".
The prospect of jail time was met with a degree of incredulity, but Liberal senator James Paterson insisted it was no empty threat.
"It's a very serious (threat) and one which the Senate and its committees must be prepared to follow through on, because otherwise witnesses who are required to appear before the Senate will just choose not to comply in the future," he told Sky News.
"It is incredibly important ... he gives evidence because only he is in possession of some of the information required to get to the bottom of this issue."
As hearings wrapped up on Thursday, Foreign Minister Penny Wong formally declined to hand documents relating to the Qatar decision to the inquiry.
It had been heard Transport Minister Catherine King had consulted Senator Wong over the application this year.
"Documents found to potentially be within the scope of the order would prejudice Australia's international relations," her statement read.
"Disclosure of such documents would not be in the public interest as it would harm Australia's ability to negotiate international agreements between governments by undermining the trust and confidence in which such agreements are negotiated."
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