SAS said some 230 flights and 27,000 passengers would be affected by Monday's action, adding to the 50,000 travellers who have been stranded since Swedish pilots walked out on Friday.
Flights between Stockholm and Athens, Brussels, Dublin, Frankfurt, Geneva, London and Paris were cancelled on Monday.
The strike began after Swedish pilots based in Stockholm rejected the airline's offer of a 2.2 percent wage increase, insisting on a hike of 3.5 percent, and attempts by a mediator to broker a deal on Sunday failed.
“The Swedish pilot union has turned down a second bid by the mediator, which SAS accepted,” said the airline.
The walkout comes during peak travel season, and has hit charter group hard.
The strike began on Friday at 6pm after the pilots' union rejected a proposed 2.2 percent wage increase, insisting on a hike of 3.5 percent.
The employers' organisation however said the pilots' overall demands, including employment contracts offering greater job security, would entail a ten percent cost increase.
“That would mean a cost increase of almost 100 million kronor ($12 million) a year for SAS. We can't afford that given the current competition,” SAS chief executive Rickard Gustafson told news agency TT.
SAS said it had not calculated how much money it was losing because of the strike, but financial analysts estimated it was costing the airline at least $1.2 million a day.
Analysts said the losses could be even greater if customers were to lose confidence in the airline's dependability because of the strike.
“SAS has to weigh the loss of prestige against the consequences of higher wage costs… People might be hesitant to choose SAS next time,” air industry analyst Matts Hyttinge told TT.