Icelandair Group plans to resume services on 24 May, assuming that predictions on the progress of the Grimsvotn volcanic ash cloud hold true.
Keflavik International Airport, the airline's base, has been closed since 0900 on 22 May because of the ash cloud, which is covering Iceland and has resulted in the closure of Icelandic airspace.
Icelandair said the latest weather and ash forecasts indicate that conditions should allow Keflavik to reopen later on 23 May and that, if weather predictions are accurate, its flights will be back on schedule the following day.
It added that if there are no further disruptions due to the eruption, the impact on its finances should be minimal.
Colin Brown, director of engineering at the Institution of Mechanical Engineers, pointed out that the Grimvotn volcano differs from Eyjafjallajokull, which spewed the volanic ash which caused airspace closures across Europe in 2010, because Grimvotn "typically has produced molten lava rather than fine ash in the past".
He added: "This, combined with the fact that winds aren't currently pushing any of the ash produced towards the UK, means that it is very unlikely that UK airspace will have to be closed."