Greek depositors won't be forced into a "bail-in" after top banks raised enough capital to avoid having to seize their clients' assets, officials said Tuesday.

The banks raised enough fresh capital to get by on their own, or at least qualify for public funds making up any shortfall, they said.

"There won't be a bail-in," Bank of Greece Governor Yannis Stournaras told journalists.

Burdened by non-performing loans and constrained by capital controls imposed in June, Greek banks have seen their capital wither and been living under the threat of being forced to seize deposits as their Cyprus counterparts had been in 2013.

Under the prodding of the European Central Bank, the nation's top four banks launched at the beginning of November a drive to raise fresh capital, with a bail-in possible if they failed to raise enough to make them eligible for the injection of public funds.

A government source said Monday that the four banks had raised over 5.0 billion euros ($5.3 billion), and government spokeswoman Olga Gerovassili later said only "around 5.7 billion euros" of the 10 billion euros in bailout funds that the EU has earmarked for bank recapitalisation would be needed.

"According to available data, two systemic banks were successful in completely covering their recapitalisation needs among private investors," Gerovassili said in a statement.

The other two raised enough private money to allow the injection of public funds, with around 5.7 billion euros needed to restore their capital to a level considered by regulators as sufficient to withstand possible economic shocks.

Banking sources said Eurobank and Alpha Bank were successful in raising enough private funds, while Piraeus Bank and National Bank of Greece will need an injection of public funds.

The ECB had evaluated their capital needs at between 4.4 and 14.4 billion euros depending upon economic conditions.

Greece's government undertook sufficient measures last week to unlock the 10 billion euros earmarked for bank capitalisation in the 86-billion-euro bailout it agreed with its eurozone partners in July.

The bailout allows for up to 25 billion euros for recapitalising Greece's banks, but forecasts that such a sum would be needed to put the country's banks back on their feet "have turned out to be completely false", said Gerovassili.