"The only way to fly responsibly right now is not to fly," said Hiske Arts, who is leading the campaign by Fossil Free Netherlands.
In preliminary hearings, its lawyers argued "fly responsibly" ads were well-intentioned.
KLM says it has already discontinued 19 communications it says form the core of the Fossil Free suit.
Its "fly responsibly" web page now re-routes customers to a message that reads: "Air travel is currently not sustainable.
While advertising authorities have banned some ads, they say airlines should be allowed to discuss improvements in order to prevent "greenhushing", or allowing the issue to disappear from discussion.
Persons:
BEUC, Dimitri Vergne, Laurent Donceel, Lucas Boudet, Toby Sterling, Joanna Plucinska, Mark Potter
Organizations:
Hiske, Fossielvrij, Dutch, KLM, Fossil, Hiske Arts, Fossil Free Netherlands, European Commission, Air France, Schiphol Airport, Airlines, Advertising Standards Association, Thomson
Locations:
Netherlands, Amsterdam, Europe, AMSTERDAM, LONDON, Brussels, London