It comes as the Greek government and its international creditors
blamed each other for failing to reach a deal over economic reforms.
That failure is holding up the release €7.2bn in bailout funds.
About €30bn was withdrawn from Greek bank deposits between October and April, the central bank added.
The central bank also warned the country's economic slowdown would accelerate without a deal.
"Failure
to reach an agreement would... mark the beginning of a painful course
that would lead initially to a Greek default and ultimately to the
country's exit from the euro area and, most likely, from the European
Union," the Bank of Greece said in a report.
"Striking an agreement with our partners is a historical imperative that we cannot afford to ignore."
Despite
the warning, Greek shares rose 0.8% in mid-morning trade on the Greek
stock exchange. The Athens benchmark index has fallen 11% since Friday,
with bank shares worst affected.
'Solidarity'
Austrian Chancellor Werner Faymann was in Athens on Wednesday in a last-ditch bid to end the standoff.
"For
Europe to be stronger, it must show solidarity and support to any
country which needs it," he said during a meeting with Greek President
Prokopis Pavlopoulos.
His comments followed a harsher critique
from European Union (EU) Commission President Jean-Claude Juncker, who
on Tuesday accused the Greek government of misleading voters, as Greek
Prime Minister Alexis Tsipras accused the EU and International Monetary
Fund (IMF) of trying to "humiliate" his country.
Greece has two
weeks remaining to strike a deal with its creditors or face defaulting
on an existing €1.6bn (£1.1bn) loan repayment due to the IMF.
The country has already rolled a €300m payment into those due at the end of the June.
Mr Juncker said the Greek government had not told the truth about its latest reform proposals.
"I
am blaming the Greeks [for telling] things to the Greek public which
are not consistent with what I've told the Greek prime minister," Mr
Juncker said.
Mr Tsipras has said that the lenders wanted to raise VAT on electricity.
Other Greek ministers have criticised suggestions to increase sales tax on medicines.
But
Mr Juncker said: "I'm not in favour, and the prime minister knows
that... of increasing VAT on medicaments and electricity. This would be a
major mistake."
"The debate in Greece and outside Greece would be
easier if the Greek government would tell exactly what the
Commission... are really proposing," he added.
Greek finance
Minister Yanis Varoufakis claimed that EU proposals did include VAT
increases: "Juncker either hadn't read the document he gave Tsipras - or
he read it and forgot about it."
'Criminal responsibility'
Mr
Tsipras accused the EU and IMF of wanting cuts to pensions and tax
rises to "humiliate not only the Greek government... but humiliate an
entire people".
The IMF bore "criminal responsibility" for austerity measures that had plunged the Greek economy into recession, he added.
Meanwhile,
White House spokesman Josh Earnest said that both Greece and its
creditors should aim to restore the Greek economy without disrupting
global financial markets.
The Greek central bank urged the EU to
spell out promises of debt relief to Greece - a key demand from Athens -
in greater detail.
The bank added: "Our top priority right now
should be to create, as soon as possible, those conditions that would
enable the Greek economy to benefit from the favourable global economic
environment and the highly accommodative monetary policy at the euro
area level and speed up a sustainable return to global capital markets."
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