The cloud of volcanic ash from Icelandic Grimsvötn is forecast to reach Sweden's west coast during the late afternoon/evening on Tuesday, according to the latest forecasts.
"The ash from the volcano can come in over the west coast late in the afternoon/evening. This can have a certain impact on air traffic," the administration wrote in a statement at Tuesday lunchtime.
"Travellers with queries are advised to get in contact with their airlines."
The administration has begun to work according to the operative routines established to deal with the eventuality of an ash cloud sweeping across Swedish air space and impacting air travel.
The Swedish Transport Agency (Trafikverket) is the authority which would decide on restrictions.
Scientists expressed hope on Tuesday morning that the volcano's activity is calming down.
“We can see signs of decreased activity,” said seismologist Reynir Bödvarsson of Uppsala University to news agency TT.
Bödvarsson doesn't know if the trend will continue but thinks that there is reason to be hopeful.
“The activity could be calming down,“ he said to TT.
The Swedish Meteorological and Hydrological Institute (SMHI) is following the situation with the help of the UK's Met Office.
“At the moment the ash cloud is moving east. But there is also rain, which means that the ash will be diluted. As the cloud has moved in over Scotland it has been possible to measure fallout and decide concentration,“ said Jesper Blomster, meteorologist at SMHI to TT.
It is still too early to say if the fallout will affect air traffic. According to SMHI it will depend on the concentration of ash in the cloud.
And according to Blomster, it is only at the highest concentration of ash that air traffic is affected. He thinks that is unlikely to reach other big airports than Gothenburg's Landvetter and Vänersborg's airport in Trollhättan.
“The high level of ash concentration is estimated to reach Landvetter, and a medium level Trollhättan, but at the moment it doesn't look like other airports will be affected,” Blomster told TT.
The greater Stockholm area may be affected later in the week, according to an SMHI estimate.
The cloud of ash has already reached Norway. Medium levels of ash is expected over the south-western parts of the country and has made airplanes and helicopters from airports Stavanger and Karmoey be grounded from 8 am Tuesday morning.
“We never thought that the ash would reach us so quickly but strong westerly winds has brought it here,” said Norwegian airport operator Avinor's CEO Dag Falk-Pedersen to Norwegian TV.
According to Swedish airport operator Swedavia, it is still not certain whether the clouds of ash will affect Swedish air traffic.
“From the latest information we received Arlanda will not be affected, but some domestic destinations might, depending on how the ash spreads,” Anders Bredfell, head of information at Swedavia Arlanda told daily Svenska Dagbladet (SvD).
The eruption of the Grimsvötn volcano in south-east Iceland is reported to be more extensive than the eruption of the Eyjafjallajökull volcano in 2010 which caused weeks of air travel chaos across Europe.
When Eyjafjallajökull erupted, 375 airports were closed and 100,000 flights were cancelled all over Europe. Despite the severity of this year's eruption changes in guidelines and routines render it unlikely that the disruption will be on similar levels, according to several observers.