Airlines pressing to fly
The carriers are desperate to get back into the skies. Their losses are rising. Some now say they are collectively losing $250m (£163m; 185m euros) a day.
What they are doing is challenging the national civil aviation authorities to ease restrictions.
Here is Wolfgang Mayrhuber, Chief Executive of the German carrier Lufthansa: "No-one wants to fly through a volcanic ash cloud. But what we have seen in the past few days is anything other than a serious danger."
Two German airlines, Lufthansa and Air Berlin, say the decision to close airspace has not been based on proper testing.
They have flown aircraft, without passengers, in skies strewn with volcanic ash. One official said afterwards "we didn't find a scratch".
Lufthansa's view is that the ban is based too heavily on computer calculations.
said "we must move away from the blanket closure and find ways to flexibly open airspace". IATA says the European response has been "inadequate".
In IATA's view there have been "missed opportunities" to fly safely. Decisions, they are demanding, should be based on "real situations and not theoretical models". In their view the economic impact is greater than after the 9/11 terror attacks in 2001.
What authorities are doing is following rules established by . Brian Flynn of , says "the rules need to be adhered too and guidelines interpreted at continental level."
It is the interpretation of those guidelines that will be at the heart of meetings held today. Are they too severe? The Dutch Transport Minister, Camiel Eurlings, says "Europe's response to the ash cloud has been too severe."
However, as one official observed in relation to the UK, "most of the layers of volcanic ash cloud remain dynamic". The picture changes from hour to hour and that is why there is a patchwork of openings and closings.
The situation is very difficult to co-ordinate. So northern Italy's airspace was closed just two hours after opening.
And then there is the risk factor. The German Transport Minister, Peter Ramsauer, is quoted as saying "it would be cynical to put airline profit before safety".
So the dilemma: weighing risk. At stake are passengers' lives. What may emerge from a number of meetings today is greater flexibility in interpreting guidelines.
A reminder also of how difficult it will be to get people home once routes re-open. Tim Jeans of Monarch Airlines, that has 60,000 passengers abroad, said the logistics of getting them home would be enormous. "To think we can simply get people through the Channel Tunnel or on ferries is entirely unrealistic."
Hence the deployment of three British Navy ships to help stranded passengers.
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