The volcano Grimsvotn began erupting on Saturday. Thick volcanic ash blocked out the sun, plunging a town in southern Iceland into darkness.
The ash could pose a risk to airliners, and that's forced President Barack Obama to cut short his visit to Ireland. The president will fly to London Monday night instead of Tuesday.
The cloud of ash is expected to reach Ireland and Scotland sometime Monday evening. A Scottish airline has cancelled three dozen flights it had scheduled for Tuesday
Iceland's main airport Keflavik was due to reopen at 11 a.m. Monday after being closed for almost 36 hours.
"The outlook is good for Keflavik and other Icelandic airports in the coming 24 hours," said a spokeswoman for the airport. "We don't have a forecast for after that so we wait and see."
Officials say they don't expect the problems caused by the Grimsvotn to be as great as that caused by another Icelandic volcano last year. Last year's eruption led to the grounding of almost all air traffic in Europe for several days amid fears that the ash could cause engines to stall.
Many airlines said authorities overreacted and overestimated the danger to planes from the abrasive ash last year. Authorities say systems and procedures have been improved, and the ash is currently not expected to move into continental Europe.
Britain's Civil Aviation Authority said authorities this time would give airlines information about the location and density of ash clouds. Any airline that wanted to fly would have to present a safety report to aviation authorities in order to be allowed to fly.
The Associated Press contributed to this story