The head of the International Air Transport Association (Iata), Giovanni Bisignani, said the impact of the shutdown had been "devastating" and governments "must take their responsibility" and help carriers.
Eurocontrol said it expected about 22,500 flights to have taken place on Wednesday, out of a normal weekday total of 28,000.
"It is anticipated that almost 100% of air traffic will take place in Europe" on Thursday, the agency added.
At London's Heathrow airport, Europe's busiest, traffic ran at 90% normal service on Wednesday.
Many night flights are being allowed temporarily to help clear the backlog of stranded passengers.
Camping at New York's JFK airport
Transatlantic services have returned to their normal level, with 338 flights arriving in Europe on Wednesday, Eurocontrol also said.
German airline Lufthansa said it would fly at full capacity by operating about 1,800 flights on Thursday, up from about 700 on Wednesday.
Air France says its long-haul flights are now departing as normal, although services in parts of northern Europe remained suspended.
Denmark, Norway and Sweden - among the countries previously worst affected by the ash cloud - have now lifted the last of their bans.
Some airspace restrictions remain over Finland and some remote Scottish isles.
The flight bans were imposed by most European countries because in the high temperatures of an engine turbine, ash can turn to molten glass and cripple the engine.
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