"Over 800 of the 1,300 have said that they will return to work," said SAS press officer Malin Selander.
The Danish cabin crew went on strike four days ago following a management decision to transfer 147 employees to SAS subsidiary company Cimber, which has less generous working conditions.
The strike caused major disruption to air traffic in and out of Copenhagen Airport, which is used by many Swedes in the south of the country.
The strike was ruled illegal by the Danish Labour Court and SAS management threatened the strikers with dismissal if they did not return to work by midday today. Shortly after 11 a.m., reports in the Danish media said that the strike had been called off.
So far on Monday, an estimated 50 flights to and from Denmark have been affected by the strike action.
Meanwhile in neighbouring Norway, airline Norwegian has also been hit by strike action, this time by 70 pilots, who have walked out in a dispute over pay and conditions.