"We are demanding a lot but there is no other way. This truly is our final call if there is to be an SAS in the future," Gustafson said.
In addition, the company plans to raise additional millions by selling Norwegian subsidiary airline Wideroe, ground handling services and other assets. The moves would see SAS' workforce shrink from 15,000 to 9,000 employees.
The governments of Sweden, Denmark and Norway own 50 percent of SAS, with the rest owned by private shareholders including Sweden's powerful Wallenberg family.
The announcement came as SAS presented its third-quarter results, which showed net profit doubling to $64 million and sales rising 5 percent to $1.6 billio).
SAS was pressed to make forceful cuts to ensure credit lines from the Scandinavian governments and major banks. The earnings report had been due last week, but the company postponed it as it negotiated extending a crucial credit facility.
On Monday, SAS said it had reached a deal to expand the credit facility and extended its term until March 2015, providing it can agree on the savings cuts with labor unions.
"We haven't made money in a number of years and we cannot continue to operate if we do not demonstrate that we can earn money and make a profit," Gustafson said in Stockholm, where the company is headquartered. "Our credit providers have said that we give you this chance to turn the company around."
Bente Sorgenfrey, of the FTF union which represents most of the 2,000 cabin and ground crew in Denmark, called the plan "violent." In Norway, union spokesman Asbjoern Wikestad told broadcaster NRK that it was "not possible to cut more."
SAS has been hurt by a combination of sagging demand due to a global economic downturn, high costs and competition from low-cost carriers. Last week, Norwegian Air Shuttle, which has competed with SAS in northern Europe, announced it will start next May its first long-haul flights to New York and Bangkok from Oslo and Stockholm.
Norwegian Air Shuttle has aggressively been challenging SAS rather than trying to compete with other low-cost airlines.
SAS is not the only airline to be struggling, particularly in Europe, where the financial crisis has been hurting business. Last week, the International Airlines Group warned its Spanish carrier, Iberia, would cut 4,500 jobs, 25 aircraft and cut salaries.
"Like the rest of the aviation industry SAS is going through a very difficult period. The economic crisis, high fuel prices and tough competition has for several years pushed earnings," Danish Finance Minister Bjarne Corydon, said. "The implementation of (the plan) is an indispensable prerequisite for SAS' future."
Karl Ritter in Stockholm contributed to this report.