The European Central Bank on Wednesday raised the maximum emergency funding that Greek banks can obtain by 1.1 billion euros ($1.24 billion), a banking source told AFP.
The increase -- which brought the overall ceiling on Emergency Liquidity Assistance (ELA) to 84.1 billion euros -- came after a stark Bank of Greece warning that the country could crash out of the eurozone unless it can conclude loan talks with its EU-IMF creditors by the end of the month.
The banking source said the increase was "sufficient" to meet bank needs but did not divulge the total level of funding available to them this week.
With Greece gripped by uncertainty after five months of talks, the nation's banks have slowly been deprived of funds.
The central bank said Greek business and private bank deposits had fallen by nearly 30 billion euros between December and April, to 128 billion euros.
The ECB last week increased its assistance by 2.3 billion euros.
But it has also brought pressure to bear on Greece to end the deadlock.
The ECB has turned down the government's requests to allow its banks to increase their spending on state bonds.
And there are continued fears that the ECB could demand additional collateral from Greek banks in return for its support.
The radical left government in Athens, elected in January on an anti-austerity ticket, has submitted a series of alternative reform proposals to the creditors.
But the EU has submitted counter-proposals demanding additional savings which Prime Minister Alexis Tsipras has rejected as "absurd" and "humiliating".
All eyes now are on a meeting of the 19 eurozone countries to take place Thursday in Luxembourg.