The preacher - who lives in a secluded compound in rural Pennsylvania and whose foundation runs a global network of schools, charities and media interests - has strongly denied the accusations against him.
In a statement signed by the airline's media relations unit, Turkish Airlines stressed that it stands "united with all of the heroic and honourable Turkish people" against the coup plotters' "malevolent illegal attempt".
"Under any circumstances, we have and will continue to fulfil our responsibility to contribute to democracy."
EU Commission President Jean-Claude Juncker questioned Ankara's long-standing aspiration to join the EU. "I believe that Turkey, in its current state, is not in a position to become a member any time soon and not even over a longer period," Juncker said.
Juncker also said that if Turkey reintroduces the death penalty - something the government has said it must consider, responding to calls at public rallies for the coup leaders to be executed - it would stop the EU accession process immediately.
- AFP, AP