Two of Greece's four big banks, Piraeus and National, will need 5.7 billion euros ($6.1 billion) of recapitalisation money from the eurozone to help plug a capital shortfall, well below initial forecasts, the government said.
Rival Eurobank and Alpha managed to raise enough funds through share sales to private investors to plug their own capital gaps.
Overall the four banks were found to have a combined capital shortfall of 14.4 billion euros under the so-called adverse scenario in a European Central Bank review last month.
"According to the latest data, two systemic banks managed to cover all their capital needs from private investors," government spokeswoman Olga Gerovasili said on Tuesday.
"The other two … will need about 5.7 billion euros from the Hellenic Financial Stability Fund to conclude the process," she said in a statement, adding this would put to rest worries that current account holders may have to foot part of the bill.
"The success of the recapitalisation process … puts an end to speculation about a haircut in deposits."
Under new European rules that come into force in January depositors with more than 100,000 euros, as well as shareholders and bondholders will have to bear losses before public money can be used to prop up a bank.
A European official last week estimated the Greek banks would need between 6-9 billion euros from the eurozone.
The latest bailout deal agreed by Greece and its international creditors in August allocated up to 25 billion euros for bank recapitalisation, but Gerovasili said that estimate had proved "completely wrong."
Piraeus and National also sold shares to investors last week and put in place measures to lower their capital needs but, as expected, could not cover the whole shortfall identified by the ECB under its most pessimistic scenario.
Despite the lower-than-forecast need for external help, Greek banks are not out of the woods, some analysts say. Standard & Poor's said last week the recapitalisation of the four top banks would only be enough to absorb the losses they were expected to post over the next 12 to 18 months.
Greek banks are still subject to capital controls that were first introduced last June after months of wrangling between the government and creditors led to a 40 billion euro deposit run.