The European Central Bank on Wednesday raised the maximum emergency funding that Greek banks can obtain by 2.3 billion euros ($2.6 billion), a banking source said.
The increase -- which brought the overall ceiling on Emergency Liquidity Assistance (ELA) to 83 billion euros -- came as Greece raced against time to conclude marathon talks with its EU-IMF creditors on a new loan deal.
Taking into account other unused amounts, Greek banks have a total of 3.0 billion euros in funding available to them this week, the banking source added.
With the Greek economy gripped by uncertainty over the five-month talks, the nation's banks have slowly been deprived of funds.
Private deposits fell by 4.2 billion in December, 12.8 billion in January -- when the new radical leftist government came to power -- 7.6 billion in February, 2.2 billion in March and 4.7 billion in April, according to official figures.
The outflow is believed to have continued in May.
The ECB sharply increased its assistance this week, compared to a 500-million-euro rise it made last week.
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 scathingly rejected Athens's new bailout reform plan Wednesday.
Greek Prime Minister Alexis Tsipras now hopes to arrange a meeting with the leaders of Germany and France on the sidelines of an EU-Latin America summit in Brussels on Wednesday to keep hopes of a deal alive.