IAG declined to forecast how much it would fly from July.
Palma flights should be operating normally because of minimum services requirements.
Vueling in particular will be increasing the number of seats for flights with the mainland, while adding new routes to France and Switzerland.
The incident involving passengers who spoke Catalan on a Vueling flight was raised in the Balearic parliament yesterday.
The Balearic government has opened proceedings to demand compensation from Vueling for cancellations.