Greece has put a senior judge in charge of an emergency government to lead it to new elections on 17 June.
Bankers, meanwhile, have sought to calm public fears after the president said political chaos risked causing panic and a run on deposits.
Political leaders failed to form a government following an inconclusive parliamentary election on 6 May, leaving the state with its coffers almost empty and no elected cabinet in place to satisfy lenders it deserves the money needed to stay afloat.
After meeting President Karolos Papoulias, heads of various parties that won seats in parliament named the new interim leader as Panagiotis Pikrammenos, who runs the supreme administrative court.
A new poll confirmed that radical leftists who reject a bailout agreed with the EU and International Monetary Fund are now poised for victory, and the establishment parties that agreed the rescue are sinking further after an historic wipeout 10 days ago.
The leftists argue they can tear up the bailout and keep the euro.
However, European leaders say if Greece fails to meet promises to them, lenders will pull the plug on financing, driving Athens to bankruptcy and a swift exit from the EU single currency.
Meanwhile, the man who negotiated the biggest debt writedown in history has said a Greek exit from the euro would be "somewhere between catastrophe and armageddon".
International Institute of Finance chief Charles Dallara said a Greek default on its official lenders would wipe out the entire capital of the European Central Bank, as Greek obligations to the ECB are more than double the central bank's capital.
Speaking at the Institute of International and European Affairs in Dublin, Mr Dallara said a slower pace of fiscal adjustment was needed in Greece and other Southern EU states, such as Spain, Italy and Portugal.
As the prospect of Greece being forced out of eurozone seems ever more real, Greeks have been withdrawing hundreds of millions of euros from banks in recent days.
However, there has so far been no sign of a run on bank branches in Athens.
On Monday, according to an official account, the president told party chiefs that figures collated by the central bank headed by George Provopoulos showed savers withdrew at least €700m from banks.
''Provopoulos told me there was no panic, but there was great fear that could develop into a panic,'' minutes of the cabinet meeting quoted the president as saying.
"Withdrawals and outflows by 4pm when I called him exceeded €600m and reached €700m," he said. "He expects total outflows of about €800m, including conversions into German Bunds and other such things."
Elsewhere, Taoiseach Enda Kenny said Greece is in quite a serious situation and the country is experiencing a new wave of capital flight.
Mr Kenny said Ireland is very different as the economy is stabilising, deposits are returning to the banks and it is facing in the right direction.
