The shares were 6.5 percent firmer at 23.61 euros by 3:16 a.m. EDT. The stock closed down 15 percent at 22.18 euros in Paris on Wednesday.
SocGen's bonds weakened further, however. Spreads on its bonds due in 2016 widened by 45 basis points to the benchmark swaps-plus 260 basis points. The cost of insuring its debt against default also rose, with 5 year Credit Default Swaps 16 basis points wider at 350 basis points.
Rumors about a French sovereign debt downgrade, an expanded bailout for Greece that would hurt French banks, and a government bailout of SocGen, pulled shares of France's second-largest bank down in the heaviest volume since the 2008 financial crisis.
SocGen CEO Frederic Oudea dismissed the rumors as absolutely rubbish in an interview with CNBC television after the market closed, adding rumors about a downgrade of France's sovereign debt rating were very strange and contrary to the reality of the situation.
In an interview with Le Figaro newspaper published on Thursday, Oudea said the bank had come under a series of attacks in the stock market.
He added that the bank had not experienced any losses in particular in the past few days and that its results to date were satisfying.
The market is an echo chamber: it amplifies good news, as well as bad, Oudea told France Info radio. People are scared, so the tiniest information touches off irrational fears.
To our clients, we have to tell them that these rumors are baseless and that they can have confidence in Societe Generale. They should not listen to this stuff, which is totally baseless.
This is the latest stumble for SocGen, which was the weakest of the major French banks in Europe's stress tests of its lenders last month.
Investors have speculated it may have to raise about 3 billion euros to reach new global capital standards if the euro zone crisis worsens.
The bank -- still trying to rebuild its credibility after the Jerome Kerviel rogue-trader scandal in 2008 in which it lost 4.9 billion euros ($6.90 billion) -- also issued a profit warning last week.
Rival French banks also fell sharply on Wednesday, with BNP Paribas
BNP was 1.3 percent firmer at 3:32 a.m. EDT, while Credit Agricole was up 5 percent.
SocGen stock had lost 45 percent over the past 2 1/2 weeks, while BNP had dropped 29 percent and Credit Agricole had plunged 38 percent.
It is not the moment to sell, you have to calmy hold on, Oudea told France Info. All the bank shares are very low right now.
(Reporting by James Regan and Leila Abboud in Paris and Natalie Harrison in London; Editing by Dan Lalor and Andrew Callus)