"When we buy an aeroplane, we expect all the terms and conditions and performance guarantees that are in the agreement to be followed by the manufacturer.
This is not the case with the Airbus 320neo and the engine is underperforming," Baker told the Dubai-based satellite channel Al-Arabiya.
"There are other issues with the aeroplane. So unless these issues are fully resolved as per the contract that we have signed, we will not take the delivery," he said.
"If an aircraft manufacturer cannot deliver to us the contractually committed aeroplanes, then we have the right to walk away and order an alternative aeroplane," he said.
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"We always in Qatar Airways have a plan B and we will implement plan B if this problem with the aeroplane is not resolved as soon as possible."
Baker said Airbus has been behind schedule in delivering six planes this year. "This is unacceptable for us, because it is impeding our expansion plans," he said.
He had already warned in February that he may cancel an order for Pratt & Whitney engines for the A320neo ordered by the Gulf carrier.
Qatar Airways was due to take the first delivery in December of the 50 A320neo planes on order, but rejected the aircraft, citing problems with the engine.
German carrier Lufthansa took delivery instead.