"Some parts may be opened in the early hours (on Saturday), such as Arlanda. But the problem is that it remains closed further south in Europe," said Björn Stenberg at the Swedish National Aviation Authority (Luftfartsverket - LFV).
Swedish airspace is gradually opening southwards as aviation authorities track the movements of airborne volcanic ash from Iceland. Stenberg confirmed that most airports in Norrland are expected to reopen by mid-afternoon on Friday.
Air travel is however expected to remain disrupted for at least another 24 hours, according to Eurocontrol, the European Organisation for the Safety of Air Navigation.
"Swedish airspace is now gradually being reopened, starting in parts of (the northern region) Norrland," the Swedish National Aviation Authority (Luftfartsverket - LFV) said in a statement.
"Flight permission will be given gradually," it added.
The first areas being opened are, according to LFV, "west of a line from Gävle-Söderhamn to Kiruna with a southern limit at Gävle-Mora".
"The areas we have opened are in Norrland. This is because the ash cloud is not as strong there as previously," Erik Söderberg at LFV said.
LFV could not say when airports in the southern half of the country - including Stockholm, Gothenburg and Malmö - would be granted permission to clear flights for take-off.
65,000-85,000 passengers normally pass through the authority's airports each day.
Scandinavian Air Ambulance, which operates ambulance helicopters in Lycksele, Östersund, Uppsala, Stockholm and Visby, has now decided to resume service in Lycksele.
Jan Lindqvist at LFV told TV4 earlier that the outlook for the weekend depended on how much more ash is spewed into the atmosphere by the erupting volcano in the Eyjafjallajökull area of Iceland.
Countries across Europe were still plagued with air traffic problems on Friday morning.
According to the latest forecasts from the British Met Office, the cloud is moving over northern and eastern Europe. The Met Office has forecast that the ash will continue to ease over northern Swedish skies during Friday but will remain over central and southern areas until at least 2am on Saturday.
Eurocontrol expects around 11,000 flights to take off in Europe on Friday, in comparison to 28,000 on a normal day.
The airspace over the following countries was closed for air travel on Friday morning - Ireland, Great Britain, Belgium, the Netherlands, Denmark, Sweden, Finland, Estonia and Austria as well as northern France and parts of Germany including Düsseldorf, Cologne, Hamburg, Berlin and Frankfurt.
Charter travel operators have encouraged travellers to stay close to their mobile phones on Friday to follow the development of events, but had early Friday not yet cancelled any flights. Early departures have been delayed to the evening.
Most holiday travellers were able to depart for their destinations on Thursday, although many were unable to get home.
The three major operators - Apollo, Fritidsresor and Ving - had a total of 2,500 Swedish customers stranded overseas on Thursday as they were unable to return home.
Some planes never took off, while others were diverted to alternative airports, such as Hamburg, Majorca and Crete. A plane with 450 people who had been holidaying in Thailand arrived in Rhodes in Greece.
A quarter of European air traffic was canceled on Thursday.
The closure of the major airports in the UK, Netherlands and France had the most impact internationally with Heathrow cancelling 840 flights of 1,250, affecting 180,000 passengers.
The closure of Gatwick, Stansted and Glasgow is estimated to have affected 120,000 passengers. British airspace is set to remain closed until at least 6pm on Friday.
Eurocontrol said that half of the normal 600 flights between Europe and the U.S. will probably be cancelled on Friday.
The flight ban has been introduced amid fears that particles of glass and rock in the ash cloud may force aircraft engines to malfunction. Ash settling on the wings can also cause problems.
Coach operator Swebus expanded its services on Friday in response to the high demand and national rail operator SJ is continuing to try to find extra capacity for its Swedish rail services.
Car rental firms reported that they are all out of cars.
Eyjafjallajökull, the volcano near the southern tip of Iceland, erupted on Tuesday night. Shortly after 9pm on Thursday, 800 residents north and west of the volcano were evacuated from their homes as the melting glacier threatened to flood buildings in the vicinity.