The EU has moved to ease air travel curbs imposed after much of Europe's airspace was closed because of the spread of volcanic ash from Iceland.
Transport ministers said there would be a core no-fly area, another open to all flights and a third zone available for a limited service.
The move came as the UK, Germany, the Netherlands, France and Belgium said they would begin to reopen airspace.
Airline chiefs had lambasted officials over the flight ban.
Following talks with the bloc's 27 transport ministers by video conference, EU Transport Commissioner Siim Kallas told reporters in Brussels more planes would start flying from Tuesday.
EU transport commission spokeswoman Helen Kearns told the BBC they hoped to see a 10% or 15% increase in flights on Tuesday and another 10% increase on Wednesday.
"There will be a slow and progressive opening up of the European airspace," she said.
"It has been done based on the science and based on the principle that there can be no compromise on safety".
The airline industry says its losses have soared over $1bn (£650m; 740m euros), since much of Europe's airspace was closed five days ago because of ash from southern Iceland's Eyjafjallajoekull volcano.
BA chief executive Willie Walsh was the latest airline boss to call the flight bans unnecessary.
However, a Nato F-16 fighter jet suffered engine damage after flying through the volcanic ash cloud, said one US official earlier.
In the high temperatures of an engine turbine, ash can turn to molten glass and paralyse the engine.
But experts said the volcano - which erupted last Wednesday for the second time in a month - was now spewing more steam and less ash.
Britain's air traffic control body said airspace in Scotland, parts of the north of England and Northern Ireland would reopen on Tuesday.
The two main German airlines, Lufthansa and Air Berlin, were granted exemptions from the flight ban to allow them to bring home thousands of stranded passengers.
France said it would reopen Lyon airport later on Monday, before opening air corridors for flights between Paris and southern French cities, and eventually all its other airports.
Some passenger flights will be allowed to leave Schiphol Airport in Amsterdam from Monday night, said the Dutch transport minister.
Belgium said it would begin reopening the country's airspace from Tuesday morning.
The International Air Transport Association (Iata) earlier lambasted European leaders for their inaction, calling the travel chaos a mess and an embarrassment.
Iata chief Giovanni Bisignani said: "The decision that Europe has made is with no risk assessment, no consultation, no co-ordination, no leadership".
Airspace closures were costing airlines $200m a day in lost revenue, he said.
European airlines have asked the EU and national governments for financial compensation for the closure of airspace.
EU Trade Commissioner Karel De Gucht said the bloc's economy would suffer badly if the disruption continued for a long time.
"What makes me a little bit afraid is that there is no timer on this volcano," he told news agency Reuters.
But the EU's transport commissioner said there could be no compromise on safety.
The shroud of fine mineral dust particles from the volcano has spread from the Arctic Circle in the north to the French Mediterranean coast in the south, and from Spain into Russia.
Airspace was closed, or partially closed, in more than 20 countries.
Italy's civil aviation authority shut the country's northern airspace until Tuesday morning.
But airports have reopened in Austria, Estonia, Finland, Hungary and Turkey, after authorities there decided there was no longer any risk.
In Spain, where all airports were open, the government offered to let Britain and other European countries use its airports as stopovers to get passengers moving again.
The UK earlier deployed three Royal Navy warships to help pick up stranded passengers from Spain and the Channel ports.
The French railway company SNCF has said it will offer reduced fares and 80,000 extra seats between Paris and London this week.