A McDonnell Douglas MD-10 aircraft took off from London Stansted at 7.39am and entered Hungarian airspace at 9.11am.
The airline did not contact Hungarian authorities, which prompted an aggressive response.
Two Gripens took off from Kecskemet Airbase after the Hungarian air force was alerted.
By this point the flight had contacted air traffic control and the journey was allowed to go ahead.
The flight was expected to land in Doha at 2pm.
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