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He said that this year airlines are able to seek permission to fly through low and medium densities of ash if their aircraft are designed to do so.

“We won’t see a blanket closing of airspace,” he said.

The plume was drifting at a height of 6,000 to 10,000 meters (20,000 to 33,000 feet), the normal altitudes for passenger airliners, down from a maximum height of 50,000 feet Sunday, said Steinunn Jakobsdottir, a geophysicist at the Icelandic Met Office.

“The eruption has reduced,” Ms. Jakobsdottir said. “We don’t know exactly know what that means. We don’t know how fast the eruption will die down.”

The European air traffic control agency’s models showed the main plume of ash gradually extending northward from Iceland during the next two days. The cloud was predicted to arch its way north of Scandinavia and possibly touch the islands off the northern Russian coastline within the next two days.

Eurocontrol said the smaller ash plume was not expected to move further east than the western coast of Scotland.

Some airline chiefs complained that regulators had overreacted by shutting much of Europe’s airspace last year. But a study last month in the Proceedings of the National Academy of Sciences concluded the shutdown had been justified. It said the hard, sharp particles of volcanic ash blasted high into the air could have caused jet engines to fail and sandblasted airplane windows.

Jan M. Olsen in Copenhagen and Slobodan Lekic, Gabriele Steinhauser and Raf Casert in Brussels contributed to this report.