The COVID-19 pandemic has seen air travel collapse, plunging the industry into crisis and leaving carriers scrambling to secure funds to weather the slump.
SAS said the credit line should be seen as a complement to other ongoing activities to cut costs and strengthen liquidity.
"Market conditions also make it difficult to predict how demand will develop ahead of the important summer season given that customers are increasingly choosing to book their trips on short notice," SAS said in a statement.
Sweden and Denmark will guarantee 1.5 billion crowns each, the two Nordic governments said in separate statements.
"It is still the Government's position that SAS is important for Denmark's accessibility, Danish jobs, companies and the Danish economy in general," the Danish government said, adding that SAS had been hard-hit by the pandemic.
The Swedish state owns 14.8% and the Danish state owns 14.2% of SAS. The guarantee is pending European Union approval.
SAS, which is due to report second-quarter earnings on Thursday, completed a capital raising in late 2020 after a year of deep losses.
($1 = 8.3100 Swedish crowns)
(Reporting by Helena Soderpalm and Johan Ahlander; Editing by Elaine Hardcastle and Alexander Smith)