Stockholm-Arlanda Airport is set to remain open, although the Civil Aviation Authority (Luftfartsverket - LFV) could be forced to reassess the situation as a vast cloud of volcanic ash drifts towards Norway from Iceland.
LFV said all airspace south of a line running from Strömstad in the west to Nyköping in the east would be affected by the shutdown.
Airspace north of the line will remain open, while planes flying at high altitude will be permitted to cross the line.
Landvetter airport in Gothenburg opened for business on Monday but appears likely to close again in line with LFV's new guidelines.
"Arlanda has been open since 8am only to traffic north and west," airport spokesman Per Froberg told AFP. "The airport is open and remains open until further notice."
A cargo plane from the United States landed early Monday and two flights were set to leave later for Chicago and New York, he said.
Scandinavian airline SAS said a number of its cross-Atlantic flights scheduled to land in Copenhagen would be diverted to Oslo, while flights to Stockholm would likely land as scheduled.
In Denmark, aviation authorities on Monday reopened airspace to flights above 35,500 feet (10,670 metres), but said restrictions on flights below the limit would remain in place until at least 2am on Tuesday.
Finland, where all commercial flights had been grounded since Thursday, meanwhile temporarily opened airports in the cities of Turku and Tampere between 12 and 6pm.
The country's flag carrier Finnair said a flight from New York would likely land in the western city of Turku on Monday afternoon.
Airport operator Finavia however said forecasts indicated the ash cloud would remain above southern Finland, meaning the main Helsinki-Vantaa airport would remain closed to traffic.
Due to wind conditions blowing the ash cloud away from its skies, Iceland has left its airports and airspace open since the Eyjafjöll volcano began erupting early last Wednesday bringing chaos to European travel.
"There is no problem flying in and out of Iceland, and to be honest we see no indications that that will change in the next days," Iceland air spokesman Gudjon Arngrimsson told AFP.
He said the company ran five extra flights to the central Norwegian city of Trondheim on Sunday to help stranded passengers, mostly en route from North America to Europe, leave Iceland.
"Today we're flying to Oslo, Tampere and Stockholm," he said.