The head of the International Monetary Fund Christine Lagarde has warned of "extremely expensive" consequences if Greece leaves the eurozone.
Ms Lagarde called on Greek leaders to show their resolve to keep the country in the euro by sticking to its bailout deal with the IMF and European Union.
However, she told Dutch television that any Greek departure from the euro "would be extremely expensive and hard, and not just for Greece".
The IMF's sister organisation, the World Bank, said the crisis could spread beyond Greek borders to far bigger eurozone economies that are in trouble.
In a blow to confidence, the European Central Bank said it had halted liquidity operations with some Greek banks because their capital was too depleted.
That means they can no longer offer assets to the ECB as collateral for loans, and would have to seek costlier emergency financing from the Bank of Greece.
It was not immediately clear which banks, or how many of them, were affected.
ECB President Mario Draghi said that under the EU treaty, it was not his job to decide what happened to Greece.
Greek President Karolos Papoulias named supreme administrative court head Panagiotis Pikrammenos as caretaker prime minister.
The interim leader, who was sworn in at a ceremony presided over by Archbishop Leronimos of Athens, is little known. State television said he was born in 1945 and studied law in Athens and Paris.
In the early hours this morning, Mr Pikrammenos appointed senior finance ministry official George Zanias as the country's new finance minister and gave Petros Moliviatis, a former conservative minister, the foreign affairs portfolio.
As Greece's chief economic adviser, Mr Zanias has participated in numerous meetings of eurozone finance ministers and was closely involved in negotiating the country's bailout and historic debt restructuring.
Socialist leader Evangelos Venizelos said the caretaker government would have to deal with the issue of bank recapitalisation and pointed out that banks' capital adequacy was a cause for concern.
A new opinion poll confirmed that leftists who reject the bailout are poised to win the election next month, and the two establishment parties that agreed the rescue are sinking further.
The spectre of Greece quitting the single currency sent the euro and European shares to a fresh four-month low yesterday and raised the yields on Spanish and Italian debt, reflecting the risk that other European countries will be hurt.