IATA's Giobanni Bisignani: 'It's a European mess'
The international airline association has criticised Europe's governments for the way they closed airspace because of volcanic ash from Iceland.
IATA chief Giovanni Bisignani told the BBC: "This is a European embarrassment and... a European mess."
The crisis, now in its fifth day, has affected millions of passengers.
Britain sent three Royal Navy ships to bring home stranded nationals. British Airways' boss said test flights showed EU flight curbs were unnecessary.
MAJOR EU AIRPORTS 19/04
London Heathrow: Closed
Germany: Airports in Frankfurt, Munich and Dusseldorf reopening to take 50 Lufthansa flights
Paris Charles de Gaulle: Closed
Schiphol, Amsterdam: Closed
Rome: Leonardo Da Vinci International and Ciampino Airports open, limited service
Madrid: Madrid-Barajas Airport open, but excessive delays
BA chief executive Willie Walsh - who flew aboard a BA 747 on a test flight through parts of the restricted zone on Sunday - said the airline deemed the risk to be "minimal".
He is the latest airline boss to speak out against the flight bans imposed across Europe.
Mr Walsh is demanding the authorities lift the flight ban and allow the airlines themselves to judge when it's safe to fly.
The criticism came as hopes mounted for stranded passengers that services might resume.
Airspace in Scotland, the north of England and Northern Ireland was due to reopen on Tuesday, said Britain's air traffic control body.
Meanwhile, Germany's aviation authority has allowed Lufthansa to fly 50 planes back to Germany with about 15,000 passengers aboard.
Ryanair CEO, Michael O'Leary: 'We want ludicrous passenger rules suspended'
European airlines have asked the EU and national governments for financial compensation for the closure of airspace.
BA estimates it is losing up to $30.5m (£20m; 22.7m euros) a day. Air France-KLM said it was losing $47m per day.
Mr Bisignani, of the International Air Transport Association (IATA), said the scale of the crisis facing the industry was now greater than at the time of the 9/11 attacks on the US.
"The decision that Europe has made is with no risk assessment, no consultation, no co-ordination, no leadership," he said.
Airspace closures were costing airlines $200m a day in lost revenue, he said.
But EU Transport Commissioner Siim Kallas told a news briefing on Monday morning that the bloc would not compromise on the issue of passengers' safety.
EU transport ministers were holding emergency talks by video conference on the crisis.
European aviation control agency Eurocontrol said only about 30% of the normal number of flights - 8,000 to 9,000 - would operate in Europe on Monday.
Ash cloud footage and advice from Met Office Scientist Derrick Ryall
Several European airports have re-opened - including those in Austria, Estonia, Finland, Hungary and Turkey.
The authorities there decided there was no longer any danger from the ash cloud over their airspace.
But Italy's civil aviation authority has shut the country's northern airspace up to a height 22,000ft (6,700m) until Tuesday morning, after briefly opening it for two hours.
In Spain, where all airports were open, the government offered to let Britain and other European countries use its airports as stopovers to get stranded passengers moving again.
The French railway company SNCF has said it will offer reduced fares and 80,000 extra seats between Paris and London this week.
The enormous shroud of fine mineral dust particles now stretches from the Arctic Circle in the north to the French Mediterranean coast in the south, and from Spain into Russia.
It comes from southern Iceland's Eyjafjallajoekull volcano, which began erupting for the second time in a month on Wednesday.
The eruption - and the amount of ash being expelled - is now said to have diminished significantly.
But airspace remains closed, or partially closed, in more than 20 countries.
Tens of thousands of flights have been cancelled since the clampdown began, and the prospect of a return to normal air travel remains far from clear.
The flight bans came amid fears that the ash - a mixture of glass, sand and rock particles - can seriously damage aircraft engines.
A build-up of glass has been found in the engine of a Nato fighter jet in Europe, a US official says.
UK Prime Minister Gordon Brown announced the move to deploy the Royal Navy ships.
The ships HMS Ark Royal, HMS Ocean and HMS Albion are heading for Spain and unspecified Channel ports.
Hundreds of thousands of Kenyans working in agriculture, the country's largest export sector, face economic uncertainty because of the flight bans.
A huge quantity of fresh flowers and vegetables destined for Europe is in danger of perishing, says BBC East Africa correspondent Will Ross.
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