Millions of stranded travellers face further air chaos as the volcanic ash from Iceland that has closed most of Europe's airspace continues to spread.
An estimated three-quarters of flights were cancelled on Saturday. About 20 countries closed their airspace - some have extended flight bans into Monday.
Scientists say the Icelandic volcano activity shows no sign of abating.
Dutch airline KLM and German airline Lufthansa have carried out test flights to see if it is safe for planes to fly.
Britain has extended a ban on most flights in its airspace until at least 1800 GMT Sunday, air authorities have said.
KLM said its plane, a Boeing 737, had reached its maximum operating altitude of about 13km in the skies over the Netherlands, and there had been no problems during the flight.
The aircraft and its engines were being inspected for possible damage. After the results of that technical inspection the airline hopes to get permission from the aviation authorities to start up operations again.
Germany's Lufthansa said it flew several planes to Frankfurt from Munich.
A spokesman said: "All airplanes have been inspected on arrival in Frankfurt but there was no damage to the cockpit windows or fuselage and no impact on the engines."
Earlier, a spokesman for the international airline industry said: "We don't see the light at the end of the tunnel yet."
Icelandic geologist Magnus Tumi Gudmundsson told the Associated Press news agency: "It's the magma mixing with the water that creates the explosivity. Unfortunately, there doesn't seem to be an end in sight."
Graeme Leitch, a meteorologist at Britain's National Weather Service, said light winds and high pressure over Europe meant the cloud was unlikely to be dispersed soon.
"We don't expect a great deal of change over the next few days," he told AP.
The International Air Transport Association (IATA) predicted little or no improvement on Sunday.
"Right now through most of Europe we do not see many flights moving at all," spokesman Steve Lott told AFP news agency.
Airlines are losing some £130m ($200m) a day in an unprecedented shutdown of commercial air travel, the IATA says.
Eurocontrol, which co-ordinates air traffic control in 38 nations, said it expected 17,000 flights to be cancelled across Europe on Saturday, from a total of 22,000 on a normal day.
Long way home
Since Thursday, countries across northern and central Europe have either closed airspace or shut key airports as the ash - a mixture of glass, sand and rock particles - can seriously damage aircraft engines.
In the UK commercial flights have now been banned until at least 0700 local time (0600 GMT) on Sunday.
In northern France and northern Italy, airports are to remain shut until at least Monday.
Unable to catch flights, commuters across northern Europe have sought other means of transport, packing out trains, buses and ferries.
The Eurostar cross-channel rail service said it had never seen so many passengers on one day and the trains were fully booked until Monday.
I've only got enough medication for my epilepsy to last me until tomorrow, so my seizures are likely to start again unless I get access to that
George Craib, Amsterdam
The large no-fly zone also means that some world leaders will not be attending the funeral of the Polish president on Sunday.
US President Barack Obama has cancelled his visit to Poland.
German Chancellor Angela Merkel, who was due to return from a visit to the US on Friday, had to fly to Lisbon where she spent the night.
With all German airports still closed, she flew on to Italy on Saturday and is set to continue her journey home by bus.
The disruption also forced the cancellation of the inaugural Iraqi Airways flight from Baghdad to London.
US pop star Whitney Houston was forced to take a car ferry from Britain to Ireland for a concert after her flight was cancelled.
The travel chaos has been felt as far away as North America and Asia, with dozens of Europe-bound flights being cancelled.
British health officials said any effects of the ash on people with existing respiratory conditions were "likely to be short term".
Southern Iceland's Eyjafjallajokull volcano began erupting for the second time in a month on Wednesday, sending a plume of ash 8.5km (5.3 miles) high into the air.
Iceland lies on the Mid-Atlantic Ridge, the highly volatile boundary between the Eurasian and North American continental plates.