By Dina Kyriakidou and Lefteris Papadimas
Six senior members of the ruling PASOK socialist party, angered by his decision to call a plebiscite on the 130 billion euro rescue package agreed only last week, said Papandreou should make way for "a politically legitimate" administration.
A leading PASOK lawmaker quit the party, narrowing Papandreou's already slim parliamentary majority, and two others said Greece needed a government of national unity followed by snap elections, which the opposition also demanded.
Euro zone leaders thrashed out Greece's second financial rescue since last year, in return for yet more austerity, in the hope that it would ease uncertainty surrounding the future of the 17-nation single currency.
Instead, financial markets suffered another bout of turmoil on Tuesday due to the new political uncertainty and the risk that long suffering Greeks may reject the bailout.
The euro fell nearly three cents against the dollar and the risk premium on Italian bonds over safe-haven German Bunds hit a euro lifetime high, raising Rome's borrowing costs to levels that proved unsustainable for Ireland and Portugal.
European bank shares dived and the Athens Stock Exchange suffered its biggest daily drop since October 2008, with the general index shedding 7.7 percent.
European politicians expressed incredulity at Papandreou's announcement on Monday evening that took everyone by surprise, including his own finance minister.
"It's difficult to see what the referendum is going to be about. Do we want to be saved or not? Is that the question?" Swedish Foreign Minister Carl Bildt said.
In a statement issued after French President Nicolas Sarkozy and German Chancellor Angela Merkel conferred by telephone, Sarkozy's office said: "France and Germany are determined to ensure, with their European partners, the full implementation in the quickest time frame, the decisions adopted at the summit, which are today more important than ever."
The renewed uncertainty is likely to embarrass G20 host France as it tries to coax China into throwing the euro zone a financial lifeline.
Business executives in Greece expressed despair at how the country was being run and markets speculated on whether Italy will be the next euro zone country to slide into a debt crisis.
"I think this referendum will not happen. I'm hoping and praying for a government that will join other political forces."
Jean-Claude Juncker, who chairs meetings of euro zone finance ministers, refused to rule out a Greek debt default.
"The Greek prime minister has taken this decision without talking it through with his European colleagues," he said in Luxembourg.
Asked whether a Greeks "no" vote would mean bankruptcy for Greece, Juncker responded: "I cannot exclude that this would be the case, but it depends on how exactly the question is formulated and on what exactly the Greeks people will vote on."
Papandreou, whose party has suffered several defections as it pushes waves of austerity through parliament despite mass protests, said he needed wider political backing for the budget cuts and structural reforms demanded by international lenders.
But his problems deepened dramatically after the announcement.
The conservative opposition called for snap elections. "Elections are a national necessity," opposition New Democracy party leader Antonis Samaras told reporters.
PASOK lawmaker Milena Apostolaki quit the parliamentary group, reducing Papandreou's strength to just 152 seats out of 300 deputies before a vote of confidence later this week.
"It's my duty to resist this wrong political choice which divides in an effort to replace the popular mandate and threatens the country's viability," Apostolaki wrote in a letter to the president of parliament.
Fellow PASOK lawmaker Vasso Papandreou, who is not related to the prime minister, demanded a new government to ensure Greece receives the rescue funds.
"I am calling on the President of the Republic to convoke political leaders with the object of forming a government of national unity to safeguard the aid package decided on October 27 and call elections immediately afterwards," she said.
The prime minister did not even inform Finance Minister Evangelos Venizelos he was going to announce the referendum on the latest EU aid deal, a government official told Reuters.
"They must be crazy... this is no way to run a country," said a senior executive of one of Greece's biggest firms, speaking on condition of anonymity.
Elsewhere in the euro zone, politicians complained Athens was trying to wriggle out of the bailout package, concerned not so much about the fate of Greece as the possibly dire consequences for the entire currency union of the referendum.
One senior German parliamentarian suggested the euro zone might cast Athens adrift, cutting off its aid lifeline and allowing the nation to default on its huge debts.
"This sounds to me like someone is trying to wriggle out of what was agreed -- a strange thing to do," said Rainer Bruederle, a leader in Merkel's coalition.
Bruederle, parliamentary floor leader for the Free Democrats and a former economy minister, told Deutschlandfunk radio that Europe would have to consider turning off the flow of money which is keeping Greece afloat.
"One can only do one thing: make the preparations for the eventuality that there is a state insolvency in Greece and if it doesn't fulfill the agreements, then the point will have been reached where the money is turned off," he said.
On the markets, players scurried for safer investments, hammering stocks and punishing the euro.
The FTSEurofirst 300 index of top European shares was down almost four percent, due not only to the possibility of a disorderly Greek default but chaos surrounding the euro zone's attempts to stop the debt crisis spreading to more significant economies such as Italy.
Euro zone banks exposed to Greece and Europe's bigger, troubled economies, suffered particularly. Shares in France's Societe Generale tumbled 17 percent and Credit Agricole was down almost 12.5 percent.
Greece is due to receive an 8 billion-euro tranche in mid-November, but that is likely to run out during January, around the time of the referendum, leaving the government with no funds if there is a "no" vote.
A survey carried out on Saturday showed that nearly 60 percent of Greeks viewed the agreement on the bailout package as negative or probably negative.
(Additional reporting by Ingrid Melander and Renee Maltezou in Athens, Michele Sinner in Luxembourg, Carmel Crimmins in Dublin, Fiona Ortiz in Madrid, Jeremy Gaunt, Adrian Croft and Marius Zaharia in London, Jussi Rosendahlm in Helsinki and Erik Kirschbaum and Madeline Chambers in Berlin; Writing by Dina Kyriakidou and David Stamp)