European Council president Donald Tusk has told Greece to accept a debt deal with its international creditors or face default.
An emergency summit would be held on Monday to discuss the future of Greece in the the eurozone.
"The situation of Greece is getting critical," Tusk said in a video message.
"We are close to the point where the Greek government will have to choose between accepting what I believe is a good offer of continued support or to head towards default."
Meanwhile, according to a Greek banking source qouted by rte.ie the European Central Bank had hiked emergency funding for Greek banks by an unspecified amount after a request from the Bank of Greece.
He added that there was no problem with the Greek banks, and added that the bank governors were expecting a "positive result" at at the summit on Greece on Monday.
According to state agency ANA, the funding cap was increased by €3.3 billion.
The Bank of Greece had earlier insisted that the banking system of the country remained stable even amid a rush of withdrawals this week triggered by fresh deadlock in Greece's loan talks with its EU-IMF creditors.
"The governor of the Bank of Greece has confirmed the stability of the banking system, which is fully safeguarded by the joint actions of the Bank of Greece and the European Central Bank," Greece's central bank said.
Meanwhile, according to analysts, Greece's economy had shrunk dramatically since 2008 - the year before the US financial crisis fully spilled over and inundated Europe. Indeed, the economic collapse paralysed Athens' economic output much more than that of the other euro members.
By 2010, the situation had become critical and a total of five eurozone states had to seek help from the EU - Greece, Ireland, Portugal, and Cyprus formally applied for bailout programmes.
They were extended loans by the EU, the European Central Bank (ECB) and the International Monetary Fund (IMF) and in return agreed to implement austerity measures which were supervised by the creditors.
Ireland left the programme in December 2013, with Portugal following suit in May 2014.
Though the EC extended Spain a liquidity lifeline to help save its crippled lenders, the southern European country never formally entered a bailout programme, and its finances were never reviewed by the IMF.