Air services have returned to most parts of Europe, though the UK, Ireland and other northern countries near Iceland will remain under a no-fly zone until later today (NZ time).
EU authorities have created new zones with a smaller no-fly zone near to the Icelandic volcano that created huge ash clouds and a wider zone where flights would be subject to safety restrictions and checks, but no ban.
These will come into force at 0600 GMT on Tuesday (NZ time 6pm). This BBC map shows the current state of the ash clouds and aircraft movements.
The opening airspace in most of continental Europe comes after a series of high-level meetings and pressure from airlines on authorities accused of over-reacting to the dangers of volcanic ash.
The European aviation control agency Eurocontrol said it expected between 8000 and 9000 flights to operate in Europe during Monday, which less than a third of flights on a normal day.
This is less than earlier predictions that half of flights could be operating. The flight clampdown has stranded passengers worldwide and halted freight flights.
The UK has announced airspace in Scotland, Northern Ireland and parts of northern England will reopen Tuesday morning local time while Lufthansa Airlines has received permission to run 50 flights from Asia, the Americas and the Middle East to three German airports.
Scandinavian nations also allowed a handful of intercontinental flights. France has reopened Lyon airport with air corridors for flights between Paris and southern French cities to follow.
Schiphol Airport in Amsterdam has begun flights while Belgium’s airspace will begin reopening from Tuesday morning local time.
"On a national and European level, we have decided to move step by step toward a normalisation, within the framework of strict security requirements," German Transport Minister Peter Ramsauer said.
Over the weekend only a fifth of normal flights were flown. Figures released by Eurocontrol showed 80,000 fewer flights in Europe since Thursday compared with the same period a week ago.
Austria and the Czech Republic opened their airports on Monday. Some countries opened their airspace but others kept no-fly decrees in place. Italy closed its northern airspace after briefly opening it on Monday.
Spain has remained opened and has welcomed international airlines needing a European stopover. From there, travellers are sent on by road, rail and ferry.
The International Air Transport Association (IATA) has estimated the total cost to airlines at more than $1US billion so far, with daily losses in revenue running at $US250 million a day.
"This volcano has crippled the aviation sector, firstly in Europe, and is now having worldwide implications. The scale of the economic impact [on aviation] is now greater than 9/11 when U.S. airspace was closed for three days," IATA head Giovanni Bisignani said.
Air New Zealand advisory: The airline says UK air travel restrictions will remain in place until at least midday Tuesday (NZ time).
Overnight flights to London flew only as far as Hong Kong and Los Angeles. Today's movements are yet to be advised.
Nevil Gibson and agencies
Tue, 20 Apr 2010