European governments have opened up the continent's airspace to new flights, giving hope to hundreds of thousands of passengers stranded around the world.
European Union ministers have created three zones: A no-fly zone over the ash cloud; a caution zone where planes can fly subject to engine checks, and an open-skies zone.
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The changes should put more planes in the air from today, potentially bringing to an end the biggest air travel shutdown since World War Two.
The aviation industry, which is facing losses of more than a billion dollars, has criticised the official handling of the crisis.
A huge cloud of ash has blanketed Europe for almost a week, since the eruption of the Eyjafjoell volcano, forcing the cancellation of tens of thousands of flights.
Airports set to reopen
Britain and other governments have sent navy ships and deployed other measures to rescue stranded passengers.
But European air traffic control group, Eurocontrol, predicted that flights over the continent could be running normally again by Thursday.
British authorities said they would lift the flight ban from 7.00 am (0600 GMT) on Tuesday, starting in Scotland and moving south as conditions improved.
British Airways said it hoped to resume flights into and out of London from Tuesday evening.
France said it would begin to progressively reopen airports from late on Monday, with restricted flights from Paris to start from early Tuesday.
Flights over Germany remained banned until the early hours of Tuesday, but some operated with special permission.
More planes in the air
A spokeswoman for German carrier Lufthansa said it had permission to land 50 flights from Asia, Africa and North and South America, carrying 15,000 passengers in total.
Three KLM flights carrying passengers left Amsterdam-Schiphol airport on Monday for Shanghai, Dubai and New York, the Dutch transport minister announced.
EU Transport Commissioner Siim Kallas said: "From tomorrow morning on, we should progressively see more planes start to fly."
But he insisted "there cannot be any compromise on safety. All the decisions must be based on scientific evidence and expert analysis."
Nearly seven million passengers have been affected by blanket shutdowns which governments said were essential but which airlines blame for unnecessary chaos and massive financial losses.
In Europe marooned passengers juggled hellish combinations of rail, boat and road links, zig-zagging across borders in desperate attempts to make it home - whether to the other end of Europe or to the United States.
EU leaders under fire
Britain ordered its flagship aircraft carrier HMS Ark Royal and HMS Ocean and HMS Albion to pick up thousands of Britons from France - where they have come from all over Europe - and Spain.
"This is the biggest challenge to our aviation transport network for many years," Prime Minister Gordon Brown said.
Spain, one of the rare countries operating normally, struck an agreement with Britain, France and Germany to fly hundreds of thousands of their nationals back to Europe via Spanish airports.
EU leaders have come under fire for their dealing with the chaos, as forecasters predicted the ash cloud from Iceland could soon reach Canada.
"This is a European embarrassment and it's a European mess," said Giovanni Bisignani, director general of the International Air Transport Association.
Financial aid to airlines
Air France, British Airways, KLM and Lufthansa reported no problems after flights to test fears the ash cloud would destroy jet engines.
Authorities in Sweden, Croatia, Hungary and the Czech Republic announced the resumption of flights. Romania and Bulgaria announced their airspace had been reopened.
But as airlines argued their case, a senior US military official said the ash had affected one of NATO's F-16 fighter planes, which detected a glass build-up inside its engine.
Ash from volcanoes can be turned into a glass form at high temperatures when it passes through a jet engine.
Companies are losing 200 million euros (270 million dollars) per day according to the IATA.
The European Commission said it was prepared to authorise exceptional financial aid to airlines in line with regulations passed after the attacks of September 11, 2001.

