Airlines said, despite their efforts, there was no quick solution to cut down the backlog of passengers.
"Quite frankly we don't have an answer to this," said David Henderson, spokesman for the Association of European Airlines.
Shifting winds sent a new plume of volcanic ash over Scandinavia, forcing some airports to close again. The new airspace restrictions applied to parts of northern Scotland, southern Norway, Sweden and Finland, said Kyla Evans, spokeswoman for Eurocontrol, the European air traffic agency.
Some oil rig workers were trapped Thursday on platforms in the North Sea because helicopters were grounded.
A week of airspace closures caused by the ash threat to planes created the worst breakdown in civil aviation in Europe since World War II. More than 100,000 flights were canceled and airlines are on track to lose over $2 billion. The aviation crisis that began with an April 14 volcanic eruption in Iceland left millions of passengers in limbo and sparked calls for a wholesale reform of Europe's air traffic system.
Some travelers got a break. Authorities chartered a luxury cruise ship -- the Celebrity Eclipse -- to pick up 2,200 tourists in the northern Spanish port of Bilbao on Thursday and bring them back to England. A British Royal Navy ship also arrived in Portsmouth, southern England, carrying 440 troops coming home from Afghanistan and 280 civilians back from Santander, Spain.
Spain, which was mostly open during the crisis, arranged for more than 600 special flights to help move an estimated 90,000 stranded passengers out over the past three days.
KLM Royal Dutch Airlines and its partners were expanding capacity on high-traffic routes from Amsterdam's Schiphol airport in hopes of decreasing the backlog. The routes included New York, San Francisco, Atlanta, Sao Paolo, Dubai, Cairo, Singapore, Shanghai, Hong Kong, Taipei and Osaka.
In Germany, Frankfurt and Munich airports reported about 90 percent of flights operating. Fraport AG, which operates Frankfurt International Airport, said it would waive parking charges for planes stuck at Europe's third-busiest airport over the last week.
All of British airspace was open and major airports such as London's Heathrow -- Europe's busiest -- were running nearly full schedules. British Airways said all of its flights from London's Gatwick and City airports would take off, as well as the "vast majority" from Heathrow.
The U.S. Air Force said normal flights resumed at its bases in Britain, Italy and Germany.
Many trans-Atlantic planes between the United States and Europe were assigned flight paths above the ash cloud that still hovered east of Iceland, flying at over 35,000 feet (10,670 meters) high.
Scientists at Iceland's meteorological office said the Eyjafjallajokull volcano produced very little ash Thursday but remained quite active, with magma boiling in the crater. The plume of ash was below 10,000 feet (3 kilometers) and winds were not expected to take it over 20,000 feet.
Geophysicist Steinunn Jakobsdottir said volcanic ash was expected to fall south and southwest of the crater in southern Iceland in the coming days but it would not disrupt air travel between Europe and North America.
The volcano threw up magma chunks the size of cars and sent powerful shock waves into the air as an Associated Press reporter, photographer and television crew flew over it Wednesday in a helicopter.
In a black crater in the middle of a glacier, red magma thrashed about, propelling steaming blobs of lava onto the surrounding ice. Charges of gas -- which surge from deep inside the mountain through the magma and cause tremors 15 miles (25 kilometers) away -- exploded occasionally in a molten rock fireworks show.
The air around the volcano shivered with a constant, menacing growl. Bolts of lightning shot through the fumes and an eerie glow pervaded the pit of fire.
In response to the flight disruptions, Eurocontrol -- the Brussels-based intergovernmental agency comprising 38 nations -- was assembling a team of experts to analyze the lessons of the airspace closure.
EU spokeswoman Helen Kearns said Thursday the crisis had exposed serious flaws in the continentwide air traffic control system.
"Consumers and businesses have paid a high price over the past few days for a fragmented patchwork of air spaces," she said.
The EU has 27 national air traffic control networks, 60 air traffic centers and hundreds of approach centers and towers. The airspace is a jigsaw puzzle of more than 650 sectors. French traffic controllers have gone on strike to protect their lucrative jobs.
In contrast, the U.S. air traffic management system manages twice the number of EU flights for a similar cost but uses only about 20 control centers.
European governments and civil aviation authorities have defended their decisions to ground fleets and close the skies -- and later to reopen them -- against heated accusations by airline chiefs that the decisions were based on flawed data or unsubstantiated fears.
The International Air Transport Association has called on the EU to quickly compensate airlines for lost revenue, much like the U.S. government did following the 9/11 terror attacks.
IATA also demanded that the EU's strict passenger rights rules -- which force airlines to pay for hotels and meals for routine flight delays -- be relaxed to reflect the extraordinary nature of the ash crisis.
Budget airline Ryanair did a surprise U-turn Thursday and agreed to pay for stranded customers' hotel and food bills after being faced with huge EU fines if it did not.
Chief executive Michael O'Leary has called the EU travel rights rules "absurd" and discriminatory against airlines because ferry, rail and bus companies only have to pay for the price of a passenger's ticket.