Air Canada will be operating a full slate of flights to Europe today, now that ash from an Icelandic volcano is abating.

The airline warns, though, that some airspace restrictions are still in place, so some flight schedules remain subject to change.

Shifting winds have sent a new plume of volcanic ash over Scandinavia, for example, forcing some airports in Norway and Sweden to close again.

But planes are flying into all of Europe's other major airports, with every seat filled as airlines try to clear up the backlog of stranded passengers.

Eurocontrol, an air traffic control agency in Brussels, says 21,000 of the continent's 28,000 scheduled flights will go ahead today.

"At the current time, almost all European airspace is available, with a few exceptions in parts of southern Finland, southern Norway, northern Scotland, and western Sweden," Eurocontrol said.

But the agency said it could still take days to catch up with the demand created by the cancellation of 102,000 flights last week.

Many of the trans-Atlantic flights between the United States and Europe are being assigned flight paths above the ash cloud still hovering east of Iceland. Flying at over 35,000 feet keeps the planes above the current maximum altitude of the ash, which lingers at 20,000 feet.

The week-long airspace closure has cost airlines well over $1 billion. It's prompted the European Union to step up work on a new airspace management system known as the "Single European Sky" that will largely erase national borders in the sky.

The ash crisis "exposed serious flaws and that is something that probably cannot be ignored much longer," EU spokeswoman Helen Kearns said.

The EU has 27 national air traffic control networks, 60 air traffic centres and hundreds of approach centres and towers. In contrast, the U.S. air traffic management system is twice as efficient, able to manage twice the number of EU flights using only about 20 control centres, for about the same cost.

Meanwhile, the International Air Transport Association is calling on the EU to compensate airlines for lost revenue, much like the U.S. government did following the 9/11 terror attacks.

IATA head Giovanni Bisignani told a news conference Wednesday in Berlin that at one stage, 29 per cent of global aviation and 1.2 million passengers a day were affected by the airspace closure.

"For an industry that lost $9.4 billion last year and was forecast to lose a further $2.8 billion in 2010, this crisis is devastating," he said. "Governments should help carriers recover the cost of this disruption."

IATA also demanded that the EU's strict passenger rights rules -- which force airlines to pay for hotels and meals in cases of routine flight delays -- be relaxed to reflect the extraordinary nature of the crisis.

With files from Associated Press