Willie Walsh, BA's ceo, has reportedly called the current five day strike by cabin crew a "failure".
Walsh, who is attending the annual meeting of the airline cartel the International Air Transport Association (IATA) in Berlin, was quoted in British newspapers as saying the airline had flown 72,000 passengers on Sunday.
Unite, the union to which the cabin crew belong, is understood to be considering further ballots which could allow more strikes to be called next month.
Walsh was quoted in The Guardian newspaper saying: "Unite have failed to ground British Airways and we are continuing to fly and we are continuing to work.
"Yesterday (June 6) we flew over 72,000 customers on a day of strikes by Unite and, as I say, they have failed."
The current strike, the third and last of three planned five day stoppages, is now in its fourth day.
If Unite goes ahead with further ballots, they are likely to take six weeks to carry out, meaning no strikes could take place until at least mid-July.
The strike is over changes to working practices implemented by BA but now also including a dispute over travel concessions which the airline has withdrawn from striking staff.
Walsh also made clear yesterday that he will not back down on these concessions.
Unite said the stoppages had so far cost BA £140m.
It added: "Unite estimates that, despite BA's vastly expensive and divisive contingency operation, yet again over 40 per cent of BA's operation has been hit by the strike.
"Flights to important destinations in the BA schedule, including JFK and San Francisco, continue to fly but with passenger numbers severely down and some flights half empty.
"Unite has also been advised that so empty are BA's planes, they are now looking for volunteer passengers.
"This is because, as BA continues to seek volunteer crew to break the strike, it is now encountering applicants with no flight experience at all.
"Volunteers need to have flown in order to become crew, which is why BA are asking them to fly as passengers."
BA said that Unite's claims that the airline is asking volunteer cabin crew to fly on its aircraft as passengers to fill them up is "completely untrue".
"All volunteers will go on a specific test flight prior to operating as crew, but this is not on a scheduled route with commercial passengers," said BA.
"Our operation has been performing very well. We've been operating all our Gatwick and London City flights as well as 80% of longhaul flights and 60% of shorthaul flights from Heathrow. Where possible we have been standing up additional flights too."
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