The volcano has become more active in recent days
Hundreds of transatlantic flights have been cancelled or delayed by a cloud of ash from an Icelandic volcano drifting south over Western Europe.
Sixteen Spanish airports - including the international hub, Barcelona - are closed, with many flights being re-routed around the affected area.
Some areas of northern Italian airspace will be closed on Sunday morning, with Milan Bergamo among airports affected.
On average, 600 airliners make the Atlantic crossing every day.
Spain's national airport management agency Aena said the airports affected were Barcelona, Girona, Sabadell, Santiago, La Coruna, Vigo, Asturias, Santander, Burgos, Leon, Bilbao, San Sebastian, Vitoria, Huesca, Pamplona and Logrono.
The Spanish government said there was a chance the 1,200 mile (2,000km) long cloud could still affect the country next week.
"We don't rule it out and we will make alternative plans," Transport Minister Jose Blanco told a news conference.
He added that extra places on long-distance trains would be made available, and extra buses and boats were being laid on.
In the UK, some flights to Spain, France and Portugal were being affected.
At London Stansted, 22 Ryanair flights to the Canary Islands, mainland Spain and Portugal were cancelled, along with three EasyJet flights.
BBC Weather's Liam Dutton examines the ash cloud's path
Flights from Gatwick to Portugal, Alicante and Madrid were cancelled and at Heathrow some flights to La Coruna in northern Spain were also grounded.
Ryanair said that it expected flights to Milan's Bergamo airport to be disrupted by ash on Sunday morning.
Italy's civil aviation authority ENAC said some northern Italian airspace would be closed from 0800-1400 (0600 GMT to 1200 GMT), but Venice would remain open.
Last month, thousands of travellers were stranded after ash shut down airspace across Europe for five days.
Recent images have shown activity in the Eyjafjallajokull volcano intensifying.
Experts at the UK's Met Office said it was sending ash up to heights of 30,000 ft (9,100m).
Flights across Ireland and parts of the UK were disrupted earlier this week.