Speaking at the bank’s annual general meeting (AGM) in London on Tuesday, John McFarlane told shareholders that while there had been reports suggesting he may soon leave the bank, he said “the speculation is somewhat premature”.
He added that succession for his position should “take place only when the time is right”.
The chairman said that when he joined the board as chairman, he indicated plans to serve a minimum of four years.
“I have now served three, so while some might wish so, you are not getting rid of me yet,” he said, sparking shareholder applause.
The chairman also threw his weight behind Mr Staley - who is now facing a fine from City regulators over attempts to identify a whistleblower - reiterating that he had the unanimous support of the Barclays board.
However, one shareholder hit out at executives for their backing of the chief executive, saying he “should have known better than to bring shame on our bank”.
Another also asked why Mr Staley had not yet resigned.
It follows the issuing of draft warning notices by the Financial Conduct Authority (FCA) and Prudential Regulation Authority (PRA) last month over the chief executive’s attempt to identify a whistleblower in 2016.
The size of the proposed penalty has not been disclosed, but Mr Staley was given 28 days to respond to the warning notice.
Mr McFarlane pushed back at criticism of Mr Staley, saying he was “quite interested to hear who in this room has never made a mistake”.
He also said that had the whistleblower been an employee, “the matter would have been much more serious... but it wasn’t the case.
“It was a malicious letter from outside the organisation that was intended to do harm to the company and to Mr Staley.”
The chairman added that the allegations in the whistleblower letter were “untrue”.
“Jes regrets his mistake... he does not deserve to resign.”
A shareholder also warned the board over its engagement with activist shareholder Sherborne, run by Ed Bramson, which picked up a stake of over 5% last month.
Reports suggest that Mr Bramson is seeking higher returns from the investment bank and looking for bigger payouts for shareholders.
“I urge this board, if you entertain him, please do so and listen to him carefully,” the shareholder said.
“But be careful about inviting him into the house, because this is a fox that will raid our hen house ... (it is) bad for shareholders, stakeholders and more importantly bad for our customers,” the shareholder told executives.
Mr McFarlane said Mr Bramson has not made any proposals to the bank so far “but what we’ve done is arranged a meeting between him and the chief executive next week and we’ll take it from there”.
The Barclays chairman also cheered the lender’s recent success in putting the “bulk” of legacy issues behind it - including the recent settlement with the US Department of Justice (DOJ) over the sale of mortgage-backed securities in the lead-up to the financial crisis.
Shareholders have criticised Barclays’ management in recent years as profits, in particular from its investment bank, have disappointed. Mixed first quarter results last month failed to allay the concerns of some analysts.
John McFarlane said that the shareholder meeting marked a “turning point”, but agreed there was more to do. Significant investment was still needed to secure revenue growth, benefit from the digital economy and bolster defences against risks like cybercrime, he said.
McFarlane told the meeting a review had been carried out into the bank’s financing of tar sands and other natural resources, and this would be published later this year.