On Monday, the stock advanced more than 11 percent after a report said Air France-KLM, Lufthansa and British Airways were all interested in SAS, in which Denmark, Norway and Sweden together own 50 percent.
Tuesday's further gains were driven by comments from Norwegian Trade and Industry Minister Trond Giske setting out the conditions Oslo would want met for the sale of its 14.3 percent holding.
"Any deal [on the airline] must aim to maintain jobs, it must also ensure there is a good service for Norway and third, we want a good price for our shares," Giske said in a TDN Finans news agency report.
Giske added that his government was not currently in talks on a sale with either Stockholm, which holds 21.4 percent in SAS, or Copenhagen, which also owns 14.3 percent.
In late Tuesday afternoon trade, SAS shares were up 9.6 percent, while the Stockholm market overall was down 0.5 percent.
In February last year, the Swedish government said it was interested in reducing its holding in SAS at an "opportune moment" and Denmark and Norway followed suit.
SAS has been hard-hit by the rise of low-cost airline Norwegian and by plunging passenger traffic numbers in the wake of the global economic crisis. Rumours of a sell-off have been circulating since 2008, with Lufthansa seen as the most probable buyer.
Late last month, SAS shares soared on rumours that Lufthansa, already an SAS partner on some routes, could make an offer for the Scandinavian company as early as the first quarter of 2011.
An SAS spokesman reached on Monday said the company would not comment on market rumours.