London, England (CNN) -- A few dozen test flights Sunday offered hope that the skies over much of Europe may be safe for air travel, but officials made no promises that the massive disruptions due to volcanic ash are about to go away.
"The results coming from these flights is... there's no impact in the area," European Union Secretary of State Diego Lopez Garrido said.
EU Transport Commissioner Siim Kallas said if the ash cloud continues "moving as it moves, then tomorrow almost 50 percent of European [Union] space will be risk free." That would allow more flights to resume, he said. "But we'll see [Monday] what the picture shows."
Two key air travel groups issued a joint statement pushing authorities to ease flying restrictions. Airports Council International (ACI) Europe, which represents airports, and the Association of European Airlines (AEA) said they question "the proportionality of the flight restrictions currently imposed."
But an expert who has flown into the skies to check conditions said he believes it will be "a few days yet" before it's safe to fly.
A spokeswoman for KLM, one of the airlines that conducted test flights, told CNN the flights show European airspace is safe, with the exception of Iceland. CNN's Gary Tuchman in Iceland reported that there were airspace problems in eastern Iceland. In the capital, Reykjavik, flights were taking off and landing.
British Airways, which conducted a test flight Sunday, said "conditions were perfect and the aircraft encountered no difficulties." The plane will undergo "a full technical analysis" next.
European transport ministers plan to discuss the results of flight tests at a technical meeting Monday.