He said no financial details were mentioned in the letter.
According to Swedish news agency TT, SAS is concerned about Estonian Air's financial woes and believes the company needs a capital injection.
But the Estonian government has been unwilling to throw more money into the carrier given its own financial difficulties in the wake of the global financial crisis, TT said.
SAS would be willing to inject capital into the beleaguered airline but only if Tallinn sells it its shares.
"If this doesn't happen, SAS cannot take responsibility for Estonian Air's future," SAS chief executive Mats Jansson wrote in the letter, TT reported.
SAS itself has in recent months been the subject of takeover rumours after heavy losses this year.
In the third quarter, SAS reported net losses of 2 billion kronor ($260 million) compared to a profit of 701 million kronor a year earlier, as the financial crisis saps demand for travel and after a deadly crash involving its subsidiary Spanair.
The Spanair plane crash in Madrid on August 20 that left 154 people dead was expected to cost SAS some 1.95 billion kronor, SAS said.
Asked whether SAS was in a strong enough financial position to increase its stake in Estonian Air, Ternert said: "SAS is a group. We have a lot of companies. We can say we have more or less successful companies. We are not in such a bad situation."
Founded in 1946, the SAS group includes the airlines SAS Denmark, SAS Norway, SAS Sweden as well as the low-cost carriers Spanair, airBaltic, Blue 1 and Wideroe. Together they carried 33.42 million passengers last year.