"SAS Scandinavian Airlines would like to inform its customers that no SAS flights will operate to,from (or) within Denmark, Norway and Sweden today or tomorrow, April 17 and 18," the company said in a statement.
"The only exception is a few domestic flights in northern Norway (that) will operate," it added.
Irish airline Ryanair, which operates dozens of routes from Stockholm Skavsta, Gothenburg City, Västerås and Norrköping, has also cancelled all Sunday flights. The airline said services would restart on Monday at 1pm at the earliest.
Both Ryanair and SAS were offering those affected a choice of refunds or rebooking onto future flights.
SAS cancelled 635 flights on Thursday and 742 flights on Friday as virtually all airspace in the Nordic countries as well as over large parts of the rest of Europe shut down due to a huge cloud of ash from a volcano erupting in Iceland.
The cloud has caused the biggest air travel shutdown since World War II in Europe, stranding millions of passengers around the world.
SAS has refused to say how much the volcano blast had cost it but according to Danish Boarding.dk, a specialised air travel news site, it was losing around 120 million Danish kroner ($22 million) per day well above the some 10 million euros it cashes in on an average day.
The company also warned Friday it might temporarily lay off up to 2,500 workers in Norway after the weekend if flights remained grounded.
The warning was linked to a requirement by Norwegian law to give employees at least two days notice in these cases, and a company spokeswoman told AFP workers in Sweden and Denmark, where the rules are different, would likely receive a similar warning later.
"We can't fly. Our entire fleet is on the ground ... There is nothing for them to do," Elisabeth Manzy explained late Friday.
With Swedish airspace closed, travellers booked on other airlines were in no better position than those planning to fly with SAS.
The cancellations have led to increased demand on buses and trains. Both train operator SJ and Sweden's biggest bus operator, Swebus, said they had increased capacity to respond to demand. Some of SJ's high-speed X2000 routes were operating at double capacity on Saturday. Both companies said there were still tickets available on most services.