O'Leary had said that other low cost airlines like Jet2.com could go bust this winter if oil stays at $130 a barrel.
Mr Meeson said: "It won't be Jet2.com. I'm sorry Mr O'Leary – unlike you, Jet2.com has bought all its fuel for this summer, this coming winter and next summer at attractive rates."
"And because people enjoy flying with Jet2.com, we are having a great year yet again."
"Our passengers can rely upon us for many, many years to come."