The surprise IMF announcement came as the European Union told leftist Greek Prime Minister Alexis Tsipras bluntly to stop gambling with his cash-strapped country's future and take crucial decisions needed to avert a devastating default.
A Greek source told Reuters that the entire Greek delegation that had been negotiating a cash-for-reform deal had left Brussels for home on Thursday, citing outstanding disagreements.
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That could trigger capital controls and possibly send Greece hurtling towards an exit from the euro zone, with unpredictable consequences for financial markets and the European economy.
Rice said the key sticking points remained pensions, taxes and financing. The IMF technical team had returned to the US but remained "fully engaged" with Athens.
European stocks fell after the IMF comments.
Earlier, European Council President Donald Tusk spelt out an unprecedentedly forthright message to Greece's radical anti-austerity government after four months of bitter negotiations.
"There is no more time for gambling. The day is coming, I'm afraid, that someone says that the game is over," he told a news conference after chairing an EU-Latin America summit that was dominated by intense talks with Tsipras on the sidelines.
"It is very obvious that we need decisions, not negotiations," Tusk said, adding that Athens needed to be "more realistic".
Tsipras held two hours of talks with European Commission President Jean-Claude Juncker, but neither side reported any breakthrough. "Come in the torture room," Juncker told Tsipras at the start of their meeting.
EU officials later described the talks as a "last attempt" to reach a debt deal.
Asked about concerns for the process raised by the departure of IMF and Greek negotiators, an EU diplomat said: "If the process was working properly the President would not have had to have a meeting with Tsipras today."
Tsipras told reporters he had worked on bridging the remaining differences on fiscal and financing issues.
"We are working to assure an agreement which will ensure that Greece will recover with social cohesion and viable public debts," he said.
EU officials said the high-level Eurogroup Working Group, which prepares decisions for euro zone finance ministers, would discuss the IMF walkout at a meeting in Bratislava, Slovakia, on Thursday evening.
Tusk's dramatic admonition reinforced warnings by powerful German Bundesbank President Jens Weidmann and EU Economics Commissioner Pierre Moscovici that time was running out to avert a Greek state bankruptcy and possible exit from the euro zone.
Their stern tone contrasted with more optimistic noises from EU officials involved in the detailed negotiations with Greece, who said there was now a good chance of a deal in time for euro zone finance ministers' next meeting on June 18 in Luxembourg.
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