The European Central Bank should not provide stop-gap financing to Greece even if the debt-wracked country does reach a deal with its creditors, one of its governing council members, Jens Weidmann, said on Thursday.

"It should be clear to all the parties to the current negotiations that the Eurosystem (European system of central banks) must not provide bridge financing to Greece even in anticipation of later disbursements," said Weidmann, who is head of the German central bank or Bundesbank.

He was speaking a financial congress in Frankfurt.

Weidmann's comments came as Greece tries to thrash out a deal to unblock the last 7.2 billion euros ($8.0 billion) of its EU-IMF bailout before it expires on June 30 in order to meet a 1.5-billion-euro IMF loan repayment due on the same day, or risk defaulting.

The ECB is currently the sole financial lifeline keeping Greek banks -- and by extension the country as a whole -- afloat.

And it is the sole European institution seen as being able to move fast enough to step into the breach if a deal is only reached at the very last minute.

Given the dire state of its finances, Greece currently has no access to the financial markets and is solely dependent on its banks for financing.

But the banks, in turn, cannot fund themselves via the ECB's normal refinancing operations, because they are barred from using junk-status Greek governments bonds as collateral.

So, for months now, the Greek banks have been compelled to turn to the eurozone's Emergency Liquidity Assistance (ELA) for cash.

On Wednesday, a Greek bank source said the ECB increased the ELA ceiling again for the fifth time in eight days as Greek savers continued withdrawing their money in large volumes from the country's stricken banks.

But the ongoing provision of emergency liquidity is starting to raise eyebrows because, under eurozone rules, ELA is a temporary facility aimed at banks that are fundamentally solvent.

Weidmann reiterated his reservations about ELA.

"It was originally conceived as a temporary source of liquidity for financially sound banks in return for good collateral (but) has been provided for a protracted period of time and has become the banks' only source of funding," he said.

"This casts doubt on their financial solidity. The latter is especially undermined by Greek policy decisions that have sparked capital flight and large-scale cash withdrawals," he complained.

Greece's central bank has said that the deposits of Greek businesses and residents fell by nearly 30 billion euros between December and April, to 128 billion euros.

"Banks receiving ELA should be urged to do their utmost to improve their liquidity situation and be prevented from worsening it further by rolling over illiquid T-bills of their sovereign," Weidmann said.

Athens has also repeatedly asked the ECB to raise the ceiling on the amount of short-term treasury or T-bills it can issue to give it additional financial breathing space.

"When banks without access to the markets buy debt of a sovereign which is likewise locked out of the market, taking recourse to ELA raises serious monetary financing concerns," Weidmann said.

"Respecting the core principles upon which our monetary union is built is not a matter of dogmatic German stubbornness, but a key policy condition for long-term economic prosperity in the euro area and for maintaining popular support for the historic project which European integration no doubt is," he insisted.