"It needs to be crystal clear that responsibility for further developments in Greece and for any decisions on transferring financial resources lies with the Greek government and the countries providing assistance, not the ECB governing council," Bundesbank chief Jens Weidmann told a conference.
"Central banks need to show where their limits lie," said Weidmann, who as head of the Bundesbank sits on the ECB's governing council.
The ECB is currently keeping Greek banks -- and by extension the Greek economy -- afloat via its Emergency Liquidity Assistance, or ELA, facility.
But it has frozen the total amount of ELA aid at 89 billion euros ($99 billion) and earlier this week actually toughened the conditions for Greek banks to tap the liquidity.
The ECB defines ELA as support given by eurozone national central banks in "exceptional circumstances and on a case-by-case basis to temporarily illiquid institutions and markets".
The problem was that it was difficult to tell the difference between "illiquidity and insolvency," Weidmann said.
And in the case of Greece "doubts about the solvency of banks are legitimate and rising by the day," he said.
Weidmann blamed the capital flight seen in Greece before Athens closed down the country's banks on the government under Prime Minister Alexis Tsipras, which he said "has been widely criticised as an unreliable negotiating partner."
Greece has been forced to implement capital controls, limiting the amount of cash people can withdraw from their accounts to 60 euros per day.
Weidmann said he welcomed the fact that the ELA was "no longer being used to finance capital flight caused by the Greek government.
"This certainly represents a step forward, and shifts the responsibility to where it belongs: with the governments and parliaments," he said.
"In any case, the Eurosystem (European system of central banks) should not increase the liquidity provision, and capital controls need to stay in force until an appropriate support package has been agreed by all parties and the solvency of both the Greek government and the Greek banking system has been ensured," Weidmann said.
"In the event that further short-term assistance is thought to be desirable or necessary, it is up to fiscal policymakers to provide ad hoc financial support," he insisted.
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