About half of flights over Europe are expected to go ahead on Tuesday, the Eurocontrol air traffic agency says.
A limited number of flights have taken off in northern Europe after five days of a blanket no-fly zone caused by the spread of volcanic ash from Iceland.
Planes have been departing from Paris, Amsterdam and Frankfurt among others - though many flights are still grounded.
A new ash cloud spreading from Iceland has meant that most of UK airspace, including London, remains closed.
Experts say southern Iceland's Eyjafjallajoekull volcano - which erupted last Wednesday for the second time in a month - has entered a new phase and is producing more lava rather than ash and dust.
Brussels-based Eurocontrol says some 14,000 of Europe's 27,500 daily flights are expected to fly on Tuesday.
The air traffic agency's deputy director of operations, Brian Flynn, said: "The outlook is optimistic that bit by bit, hopefully in a few days' time, the situation will be restored to normal movement of air passengers in Europe."
The UK's air traffic control authority, Nats, says it is unlikely that the main airports in London will reopen on Tuesday. A few flights have taken off from Scotland and Northern Ireland and there is limited airspace open over the north of England.
British Airways says it has cancelled all short-haul flights, but is hoping to operate long-haul flights after 1600 BST (1500 GMT).
The airline said this "remains subject to the full and permanent opening of airspace".
A Nats statement said the situation remained "dynamic" and that "the latest information from the Met Office shows that the situation today will continue to be variable".
In an effort to try to take control of the situation, EU transport ministers have created a core no-fly area, a limited-service zone and an open-skies area.
The first flights left Amsterdam's Schiphol Airport late on Monday. Dutch Transport Minister Camiel Eurlings said his country was "taking a lead" in restarting flights, but warned that further suspensions might prove necessary if the situation worsened.
Swiss and northern Italian airspace has reopened. The Swiss authorities said test flights had shown a considerable reduction in the amount of ash in the atmosphere and posed no threat to passenger safety.
Flights have resumed out of Paris' Charles de Gaulle and Orly airports, which are operating at about 30% capacity.
The skies over Germany are to remain closed until 1800 GMT, with some exceptions.
The German carrier, Lufthansa, said it was planning about 200 flights on Tuesday, taking advantage of special permission to fly visually rather than relying on instruments and keeping in constant touch with air traffic controllers. - BBC