US and European markets have fallen following Monday's announcement of a Greek referendum on the latest aid package to solve its debt crisis.
Eurozone leaders agreed a 50% debt write-off for Greece last week as well as strengthening Europe's bailout fund.
But the Greek move has cast doubt on whether the deal can go ahead.
New York's Dow Jones ended the day 2.5% lower, after a mid-afternoon rally on hope that Greek MPs may block the referendum proved short-lived.
One of Mr Papandreou's MPs, Milena Apostolaki, resigned from the ruling Pasok parliamentary group on Tuesday, leaving the government with a two-seat majority in parliament.
Six other party members have called for Mr Papandreou to resign, according to the state news agency.
There are doubts whether the government will last long enough to hold the referendum, pencilled in for January.
A confidence vote is due to take place in the Greek parliament on Friday.
Earlier in the day, London's FTSE 100 had ended trading down 2.2%, while the Frankfurt Dax fell 5% and the Paris Cac 40 some 5.4%.
Shares in French banks saw the biggest falls, with Societe Generale down 16.2%, BNP Paribas 13.1% and Credit Agricole 12.5%.
Other European banks also fared badly for the second day, with Germany's Commerzbank and Deutsche Bank and the UK's Barclays and Royal Bank of Scotland all 8% to 10% lower.
In the US, Bank of America fell 6.3%, while Morgan Stanley was down 8% at the close of trading.
German Chancellor Angela Merkel and French President Nicolas Sarkozy issued a joint statement following a telephone conversation between the two leaders saying: "France and Germany are determined to ensure with their European partners the full implementation, as quickly as possible, of decisions taken by the summit, which today are more necessary than ever."
The two also said that eurozone leaders and the IMF would meet on Wednesday to hold talks over Greece.
Greek opposition parties have accused Prime Minister George Papandreou of acting dangerously, and called for an early election.
"Elections are a national necessity," conservative leader Antonis Samaras said, adding that Mr Papandreou was putting Greece's EU membership at risk.
Opinion polls in Greece suggest that most people do not support the deal and there have been demonstrations against the austerity measures across the country, some of them violent.
Mr Papandreou told a meeting of his governing Socialist party on Monday that Greek people would have the final say on the austerity package, which is designed to reduce Greek debt by about 100bn euros through a series of measures including public sector pay cuts, tax rises and falling pensions.
The austerity measures are a condition of the bailout packages from the European Union and International Monetary Fund.
Some analysts are saying that the referendum would in effect be on whether Greece should abandon the euro.
Nobel Prize winning economist Christopher Pissarides said, "If there is a 'no' vote, Greece would immediately declare bankruptcy. I do not see how Greece could remain in the euro."
There is also concern that the referendum would be unlikely to take place before January, which would create months of uncertainty for the markets.
"We cannot wait until 15 January," said Konstantinos Michalos, president of the Athens Chamber of Commerce.
"Personally, I do not think we will ever get there."
A senior member of Chancellor Angela Merkel's coalition in Germany said he had been irritated by the referendum announcement.
"The prime minister had [agreed] to a rescue package that benefited his country," Rainer Bruederle told Deutschlandfunk radio.
"Other countries are making considerable sacrifices for decades of mismanagement and poor leadership in Greece."
He added that the only thing to do now would be to prepare for the Greek state to be insolvent and try to limit the damage to Europe's banking system.
On the currency markets, the euro continued to slide, falling a further 1.3% against the US dollar.
The yield on German bonds fell to near-record lows, while the difference between the yield of German bonds and those of Italian and Belgian bonds rose to the highest since the introduction of the euro.
Earlier, the Nikkei in Tokyo closed down 1.7% and the Hang Seng in Hong Kong closed down 2.5%.
Europe's main share markets had all fallen before the referendum announcement as well, with the FTSE, Dax and Cac 40 all dropping by about 3% on Monday.