"At the moment it looks like the ash cloud will spread into southern Sweden at 9pm Finnish time, and it looks as if it will be moving east, but we don't have an estimate as to when it might hit Finland," Raine Luojus, a spokesman for the country's aviation safety authority Finavia, told AFP.
"Most likely, it won't be so thick that it would prevent flights" in Scandinavia, he added, referring to estimates based on data from the Volcanic Ash Advisory Centre in London.
Airlines meanwhile halted dozens of flights to and from Scotland Tuesday as the volcanic ash cloud blew over Britain, even forcing US President Barack Obama to revise his travel plans and leave Ireland for Britain a day early.
In Sweden, flights were expected to run almost as normal Tuesday, except for possible cancellations to and from Scotland, according to a spokesman for the Swedish airport operator Swedavia.
"There are some indications that there might be (some ash) in western Sweden but those prognosis are still very uncertain," Anders Bredfell told AFP, adding though that Swedish authorities were preparing "for the worst-case scenario."
Iceland, which was forced to close its airspace a day after its Grimsvötn volcano began erupting Saturday, had by Monday evening reopened its four international airports, including its main Keflavik airport near the capital Reykjavik.
On Tuesday, all flights from Keflavik appeared to be on schedule except the cancellation of one flight to London Heathrow and one to Manchester/Glasgow.
When Grimsvötn, Iceland's most active volcano located at the heart of the country's biggest glacier, Vatnajoekull, in the southeast began erupting late
Saturday, it shot up a plume of ash and smoke as high as 20 kilometres into the air.
In April 2010, a massive cloud of ash from the nearby Eyjafjoell volcano caused the planet's biggest airspace shutdown since World War II, with more than 100,000 flights cancelled and eight million passengers stranded.
The costs in terms of lost revenue and compensation to passengers were a body blow to the airline industry, particularly in Europe.