The strike, which started on Friday after wage talks broke down, led to the cancellation of 220 flights on Sunday affecting 26,000 passengers, many of them travelling to France where Sweden play Ireland on Monday.
"We have our full focus on finding a solution to the conflict," SAS CEO Rickard Gustavsson told state broadcaster SVT.
"I think it's very important now that both parties take responsibility and bring the situation to an end. That 26,000 passengers are affected today alone doesn't build confidence."
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Negotiations began again on Sunday to try to end the dispute.
With some 20,000 Swedes expected to travel to Paris for their side's opening Group E game at the Stade de France and a limited number of alternative flights available, some have been going to great lengths to make other arrangements.
Sweden fan Fanny Pekkari had already driven 250 kilometres from her home in Taernendo to Kallax airport in northern Sweden when she discovered her SAS flight to Stockholm had been cancelled.
Rather than turn back, she and her friends drove a further 1,100 kms to the Swedish capital to make the connecting flights to Paris via Oslo.
"At first I just wanted to curl up into a foetal position. We saw it on the Internet," she told the TT news agency as she waited for the connection in Stockholm.
A quick decision was taken to hire a car and drive to Arlanda airport north of the Swedish capital, a journey which took more than nine hours.
"We're going to see the game, no matter what it costs," Pekkari said.
(Editing by Clare Fallon)
