The European Central Bank on Tuesday raised the maximum emergency funding that Greek banks can obtain by 800 million euros ($846 million), a banking source said.
The latest move -- the second such gesture by the ECB in as many weeks -- lifts the ceiling on Emergency Liquidity Assistance (ELA) to 74 billion euros ($78 billion).
Taking into account other unused amounts, the banks have a total of 4 billion euros in funding available to them this week, the source added.
Greek banks are dependent on the ECB for financing, but the eurozone's central bank no longer accepts Greek sovereign bonds as collateral for loans.
It had done so previously under a special waiver mechanism, but rescinded that waiver until Athens' new anti-austerity government under Prime Minister Alexis Tsipras agrees a new debt deal with its creditors.
Without the waiver, Greek banks now rely solely on ELA, which is more expensive than normal central bank refinancing operations.
Greek banks have a desperate need for liquidity. Individual account holders and business account holders withdrew 25 billion euros between early December and late February on fears about Greece defaulting under Tsipras' radical government.
The pace of the withdrawals has slowed in recent weeks, according to Greek media.