The Gulf airline has ordered 50 A320neo-family aircraft and was originally due to take the first delivery in December, but rejected the jet due to what it called an engine problem and the first jet went last month to Lufthansa instead.
Asked at the Singapore Airshow to describe his concerns, Qatar Airways Chief Executive Akbar Al Baker said: "There are a lot of things wrong with A320neo, with the engines. So we have refused to accept those airplanes.
"Let me be very clear: it is not the fault of Airbus. Airbus has delivered all their part, and as you know, no airplane can fly without an engine. And they have huge issues with the engine," he said in a group interview.
"I don't want to get into the detail but Qatar Airways will not accept an aircraft with those engines unless they are very much corrected. Otherwise we have no alternative but to look at an alternate engine supply."
Pratt & Whitney competes with CFM International, co-owned by General Electric and France's Safran, to supply engines for the narrow-body Airbus jet family.
Pratt & Whitney has acknowledged teething problems on the engine but says they do not affect its 15-percent fuel savings.
"We will not cancel the A320neo order. Our relations with Airbus are very strong. We have full confidence in the neo program but yes, we could cancel the entire Pratt & Whitney order," Al Baker told reporters.
Al Baker, who has a record of criticizing manufacturers at air shows over the airline's exacting quality standards, said engines had been delivered without the desired performance.
"According to them, they're on the way to correct these issues, but I have no confidence unless I see it really happen."
Asked whether Qatar Airways had set a deadline for the problems to be resolved, he said, "Yes we have given them a deadline... Months."
Pratt & Whitney officials could not immediately be reached for comment.
In an interview with Reuters earlier, Pratt & Whitney President Bob Leduc gave further details of two problems which have affected engine startup times and faulty engine software messages, but said these were being resolved.
Pratt & Whitney is delivering according to the latest schedule, he said.
Airbus and Pratt & Whitney officials said the schedule had been slowed in the first half of the year to ensure a smooth production ramp-up.
Leduc said some 60-65 percent of the 200 Geared Turbofan engines that Pratt intends to build in 2016 would be delivered in the second half of the year.
(Tim Hepher and Fathin Ungku - Reuters)