National aviation authorities continued to send conflicting messages to airlines and passengers on Sunday. While some isolated airports, like Frankfurt, Berlin and Warsaw, cleared the way for a handful of flights heading away from the ash cloud, most flights in northern and central Europe remained grounded.

The British transportation secretary, Andrew Adonis, ruled out any immediate change, saying flights across northern Europe “will not be safe” on Monday. But Scandinavian Airlines said it planned to operate flights Sunday night from the United States to Oslo and Stockholm.

Complicating any decisions is the continued eruption of the Icelandic volcano, Eyjafjallajokull.

As the ash cloud from the volcano has spread, it has shut down airports from the British Isles to Ukraine, disrupting the travel plans of nearly seven million travelers, according to one industry estimate. Delta Air Lines, Cathay Pacific of Hong Kong, Qantas of Australia and China Airlines of Taiwan were among those that canceled Europe-bound flights through Monday.

Since the ash cloud first appeared over European airspace Thursday, more than 63,000 flights have been canceled. Eurocontrol, the Brussels-based agency that coordinates air traffic management across the region, said that 20,000 flights, out of a regularly scheduled 24,000, were canceled on Sunday.

The interruption in service, particularly across the Atlantic, comes as the industry had just started to recover from the global recession, with business and international travel picking up.

After the spike in oil prices in 2008, several airlines went bankrupt, including Eos, an all-business-class carrier that offered flights between Kennedy International Airport in New York and Stansted Airport outside London. Analysts said Europe’s legacy flag carriers, including British Airways, Lufthansa and the Air France-KLM combination, would feel the most pain from the shutdown because they have high fixed costs.