The action comes as fears increase that the country may be forced out of the eurozone and on to a weaker currency.
Greece's president Karolos Papoulias revealed the outflows of cash in talks with rival political leaders.
He said the head of the Greek central bank had told him there was no panic yet, but that this could change.
Mr Papoulias said that the central bank governor, George Provopoulos, had said that the banks' situation was very difficult and that the banking system was currently very weak.
"Mr Provopoulos told me there was no panic, but there was great fear that could develop into a panic," the president was quoted as saying in minutes of the meetings with political leaders.
Uncertainty about the country's future has intensified after Greece's political parties failed to form a coalition government this week.
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