The cancelled flights on Sunday will affect around 64,000 passengers, adding to the estimated 34,000 passengers whose flights were already cancelled on Saturday.
"We want nothing more than that the parties return to negotiations as soon as possible so that no more passengers are hit," the company's press chief Freja Annamatz told Sweden's TT newswire.
"First and foremost, we apologize," the company's Norwegian media head Knut Morten Johansen told state broadcaster NRK. "We made a decisive move yesterday by pre-canceling, so that there was more predictability today. I think we had a less chaotic situation at the airports than would otherwise have been the case."
The Scandinavian airline has been forced to ground around 70 percent of flights after 1,400 pilots went on strike over pay and conditions. The strike is estimated to be costing the company between 60m and 80m Swedish kronor a day.
"We must reach an agreement for the sake of our customers," SAS chief executive Rickard Gustafson told the Swedish newswire TT on Friday.
"It's pretty clear that it doesn't exactly improve our reputation when we're not delivering what we promised customers."
Rawaz Nermany, chairman of the Swedish Pilot's Union, told The Local that he and his union would not restart talks unless it was offered clear concessions from the company.
"Up until this moment they haven't been willing to discuss any of our demands, and that's not a renegotiation is it? Just sitting there looking out of the window with your arms folded," he said. "They have to shift their position if there's going to be any constructive dialogue."
Gustafson said he was ready to make more concessions to the pilots, but not to the extent that SAS becomes uncompetitive. "We have to make sure that the company remains competitive in the long term, otherwise it's not going to work."
Passengers booked on flights for Sunday and Monday that have yet to be cancelled are being offered compensation if they cancel them because of the uncertainty. The strike affects all domestic flights, many flights within Europe and some long-distance flights.
- SAS strike: Thousands of passengers to be hit by weekend flight cancellations
- 'It feels like we've been abandoned': Outrage as hundreds of SAS flights cancelled
- What you need to know if you're affected by the SAS strike
The company has a continuously updated page showing flights which are still expected to fly. The company has set up a dedicated page on its website carrying the latest information on the strikes.
Nermany said he and his members were not willing to put any time limits on how long the strike might last, meaning the strikes could potentially continue into and perhaps beyond next week.
"We don't want to focus on how long the strikes can continue," he said. "We are firm in our demands and we expect to see some movement from the company before we sit down at the negotiating table again."