He said the ash now is coarser than in last year's eruption, falling to the ground more quickly.
Grimsvotn's eruption in 2004 lasted for several days and briefly disrupted international flights. The volcano also erupted in 1998, 1996 and 1993.
Sparsely populated Iceland is one of the world's most geologically unstable countries, sitting astride the Mid-Atlantic Ridge, where the Eurasian and North American continental plates rub up against one another. Frequent earthquakes push magma from deep underground toward the surface, and volcanic eruptions are common. The ground is covered by hardened black lava from past eruptions and steam belches from the earth — harnessed by Icelanders for geothermal power.
Volcanic eruptions in Iceland often spark flash flooding from melting glacier ice but rarely cause deaths. Usually they only have a local impact, but when they do draw the world's attention, it's in a spectacular way.
The 1783 eruption of the Laki volcano spewed a toxic cloud over Europe, killing tens of thousands of people. Crops failed and famine spread.
In April 2010, the Eyjafjallajokull eruption prompted aviation officials to close Europe's air space for five days out of fear that the ash could harm jet engines. Thousands of flights were grounded, airlines lost millions of dollars and weary travelers slept on airport floors across northern Europe.
Some airline chiefs complained that regulators had overreacted. 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.
Scientists said there were already signs that the latest eruption was tapering off.
"The intensity of the eruption has decreased markedly overnight," Matthew Roberts of the Icelandic Meteorological Office told the BBC, saying the ash plume had fallen to about 6 miles (10 kilometers) high.
Gudmundsson said the duration of the latest eruption would probably be short.
"In two or three days, the worst should be over," he said.