By Tommy Stubbington 

Greek financial markets steadied Thursday following their sharp postelection slump, with battered Greek bank stocks rallying sharply.

Athens's main stock index climbed 3.2% as relative calm returned after Wednesday's 9.2% decline, which came as investors took fright at the radical new Syriza-led government.

Shares in Alpha Bank AE and Eurobank Ergasias SA, which fell sharply on Wednesday amid concern that depositors are moving their money out of the country, rebounded.

Gains for the battered banks came despite data from the European Central Bank showing that private-sector deposits at Greek banks fell EUR4.6 billion in December to EUR173.2 billion, the biggest monthly drop since April 2013.

The broader stock market's move higher also came despite Standard & Poor's Ratings Services downgrading its outlook for Greece's credit rating after Wednesday's close.

The move "reflects our view that some of the economic and budgetary policies advocated by the newly elected Greek government, led by the left-wing Syriza party, are incompatible with the policy framework agreed between the previous government and official creditors," S&P said in a statement.

That fueled a brief spike in government bond yields early on Thursday, suggesting investors are growing increasingly concerned about the possibility of a default. But most Greek bonds erased early losses to rise on the day. Greece's 10-year yield fell slightly to 10.34%. Yields fall as prices rise.

Spillover into wider European markets remained muted, although stocks were weighed down by a selloff in the energy sector, after Royal Dutch Shell's profit fell short of expectations. The Stoxx Europe 600 fell 0.3%, with oil and gas firms losing 2.9%.

Germany's DAX was up 0.2%, while the U.K.'s FTSE 100 fell 0.6%.

Despite the declines, European shares have outperformed their U.S. peers since the ECB last week announced it will embark on an aggressive bond-buying stimulus program.

A preference for European equities over U.S. markets is becoming more popular "but we don't think it's becoming consensus positioning wise yet, " said Deutsche Bank strategist Jim Reid.

The ECB's bond-buying program has buoyed bonds across the eurozone and helped insulate the rest of the currency area from the turmoil in Greece. Italian and Spanish bonds have weakened only modestly.

German bonds, considered the eurozone's safest, remained in high demand Thursday, with the 30-year bond yield falling below 1% for the first time.

Write to Tommy Stubbington at tommy.stubbington@wsj.com

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