Several of the routes are to countries where residents of Denmark and Sweden are not supposed to go unless it is absolutely essential, such as Greece, Spain and Italy.
From Stockholm's Arlanda airport, it will restart flights to Athens from this Saturday, and to Palma de Mallorca in Spain on June 15th.
And from Copenhagen, it will fly to the tourism hotspots of Athens, Malaga, Nice, and Split from June 20th.
Freja Annamatz, the airline's press chief, said that she still expected passengers to follow the advice of their governments, and not to travel for holidays.
“We are expecting everyone to follow the advice from the Swedish foreign ministry and the rules in the other countries,” she said.
“We see that there is a demand for journeys to a number of Mediterranean destinations. People have family or second homes and that is why there is a need for people to be able to travel to Spain, France and Greece.”
From Copenhagen, the airline will fly to destinations both to destinations in Germany, Norway and Iceland – which Danish residents can now freely travel to – and to Belgium, Lithuania, and Italy, where Danes can only travel if absolutely necessary.
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“We're slowly and safely starting up with a small summer programme, which we hope will generate some demand, which is for necessary journeys,” Sille Beck Hansen, the airline's press chief in Denmark told the Ritzau news agency.
The new routes were announced with press releases in Danish and in Swedish, and the airline has also published its full traffic programme in Swedish and Danish.
Here are the planned routes:
From June 15th:
ARN-Athens (from June 6th, Saturdays)
ARN-Palma de Mallorca (Saturdays)
ARN-Östersund (every day except Saturday)
ARN-Visby from June 18th (every day except Saturday)
CPH-Brussels (every day except Saturday)
CPH-Düsseldorf (every day except Saturday)
CPH Faroe Islands (Tuesday, Thursday, Sunday)
CPH-Hamburg (every day except Saturday)
CPH-Milan (Monday, Wednesday, Friday, Sunday)
CPH-Munich (every day except Saturday)
CPH-Palanga (Monday, Wednesday, Friday, Sunday)
CPH-Reykjavik (Monday, Wednesday, Friday, Sunday)
CPH-Stuttgart (Tuesday, Thursday, Sunday)
CPH-Trondheim (Monday, Wednesday, Friday)
CPH-Vilnius (every day except Saturday)
From June 20th
CPH-Athens (Monday, Saturday)
CPH-Frankfurt (every day except Saturday)
CPH-Split (Wednesdays, Saturdays)