"We don't want any subsidies but we want compensation since we have been forced to be grounded and it was not necessary," Wolfgang Mayrhuber told a Berlin press conference organised by the International Air Transport Association.
Around 100,000 flights were cancelled in April after EU authorities closed large parts of the continent's airspace to commercial traffic amid fears that volcanic ash could severely damage jet engines.
Airlines lost an estimated $1.8 billion dollars (€2.2 billion) as a result of the decision.
"There is probably an intelligent way to compensate airline companies," Mayhruber said.
He suggested one way would be to freeze a European emission trading scheme known as ETS that aims to cap greenhouse emissions.