Greek banks could start to run out of cash over the next two days if creditors do not agree to a new aid deal, two sources familiar with the country's financial system said.

With withdrawals from cash machines rationed to a maximum of 60 euros a day and the banks shut since last week, supplies of banknotes have been dwindling fast.

One source familiar with the country's banking system said he expected some ATM machines to start running out of money by Wednesday while the other source, a banker in Greece, said there could be two-days' worth of money left in the system.

"Cash is going to be a real problem at the ATMs tomorrow," the first source said, speaking on the condition of anonymity. "The 60 euros a day has really prolonged the life of the ATMs but actually things are looking to be much more challenging from tomorrow."

The second source, a senior banker in a Greek bank who also spoke on the condition of anonymity, said the country's cash system would grind to a halt if the Greek Prime Minister Alexis Tsipras could not seal a deal in the coming days.

Tsipras launched a fresh bid to win new funds from sceptical creditors at an emergency euro zone summit on Tuesday.

"I don’t know if the ATMs will run out of money on Wednesday or Thursday night, but if we don’t have a deal or an interim deal with Europeans we will run out of banknotes in 2 to 3 days," the banker added.-Reuters