The airline canceled around 70 percent of its flights on Friday and Saturday.
SAS is in the midst of renewing an aging fleet after spending years cutting costs in the face of competition from budget carriers such as Norwegian Air Shuttle and Ryanair.
At airports across Scandinavia stranded passengers were queuing at SAS counters to get help.
At Copenhagen Airport, Spanish teachers Juan Manuel Gonzalez and Miguel Angel, on a trip with 23 students to Chicago, had been re-booked on a flight on Saturday, but the delay was proving costly for their students.
"The kids had tickets for basketball and theaters tonight, so they won't be able to get a refund. It is a nightmare for them and they're in a very bad mood," Gonzalez said.
On her way from the Faroe Islands to her home in Frankfurt, Astrid Melbert did not know when she would be able to leave Copenhagen.
"The last two times I've been traveling, I was hit by strikes, so I thought I would book with SAS this time. See how that went," she said.
Many flights at regional rival Norwegian Air were sold out on Friday with some ticket prices on its website soaring. A flight between Oslo and Stockholm cost 9,000 Swedish crowns ($948), several thousand more than might normally be expected.
TALKS ON HOLD
SAS, whose shares traded 5.3 percent lower in Stockholm on Friday, said it hoped to resume negotiations and reach an agreement with its pilots as soon as possible.
"As a consequence of the strike, domestic, European and long-haul flights have been canceled, and thousands of travelers will be affected," it said in a statement.
SAS said it was prepared to continue to negotiate, but that if the pilots' requirements were met, it would have "very negative consequences" for the company.
Analysts at Sydbank expect the strike to cost SAS 60-80 million Swedish crowns ($6.3-$8.4 million) per day, wiping out an expected net profit for the year if it lasts for two weeks.
"The SAS pilots' strike...makes it clear that SAS is more vulnerable than we previously expected," Sydbank analysts said.
In total, 1,409 pilots from a total of around 1,500 across the three countries went on strike on Friday. Flights operated by SAS partners, which make up approximately 30 percent of all departures, were not affected, the airline said.
"The strike could have been avoided, if SAS had shown a real willingness to meet us halfway," said Rene Arpe, chairman of the Danish pilot union.
The aviation industry's employer body in Sweden said pilots held onto their "extreme wage claims", demanding a 13 percent wage increase despite what it called already high average wages of 93,000 Swedish crowns ($9,759.89) a month.
The unions dispute the figure, saying salaries start at 34,000 SEK, increasing over 25 years to 98,000 for a captain.
The SAS Pilot Group, a federation representing 95 percent of the airline's pilots in Denmark, Norway and Sweden, said in a statement it had tried to gain greater transparency about working hours.
Most pilots don't have fixed schedules and in some situations risk working seven weekends in a row, the group said, adding that pilots were prepared for a "prolonged" strike.
Close to bankruptcy in 2012, SAS was forced to sell assets and cut wages and thousands of jobs in return for a life-saving credit facility. It has posted a net profit in each of the last four years.
But fuel costs are rising in line with crude prices and European airlines face continued overcapacity and currency volatility, factors that have toppled several smaller players in the past year.
Labor tensions have also risen in the past two years as the industry faces a global pilot shortage.
That has bolstered pilots' bargaining power, as seen at other airlines including Ryanair, Lufthansa and Air France.
(Reporting by Terje Solsvik and Gwladys Fouche in Oslo, Jacob Gronholt-Pedersen in Copenhagen, Anna Ringstrom and Niklas Pollard in Stockholm; editing by Jason Neely and Kirsten Donovan)
By Esha Vaish and Andreas Mortensen