Officials announced on Monday that the banks would remain closed until Thursday, as the European Central Bank (ECB) slowly tightened a noose on its funding.
The daily withdrawal limits were to remain unchanged at 60 euros ($66) per account daily.
Reports said Greek banks were now operating "under siege", with one major Athens bank only able to keep its ATMs open on Monday after two major companies deposited their payrolls in cash.
"The banks are living day-to-day and hand-to-mouth," Sources said
"They believe they have enough to keep going until Wednesday, possibly Thursday, but only under the capital controls (withdrawal limits)."
The ECB has maintained its emergency liquidity lifeline for Greek banks, however it raised charges on collateral the banks require to present for funds, effectively devaluing the banks' assets and making them less able to borrow against their collateral.
"The situation is becoming financially worse, not just more politically difficult," our correspondent said.
Greece last week defaulted on a $1.8bn repayment to the International Monetary Fund, and on Sunday, in a referendum, the Greek people voted to say "no" to Europe's bailout deal.
