Former ECB vice-president Lucas Papademos arrived at the presidential palace for talks involving outgoing Prime Minister George Papandreou, opposition leader Antonis Samaras and the leader of a smaller party.
Greek shares rose on the possibility that Papademos, a respected figure in European capitals, might take the helm of the interim government which will rule until early elections.
The stock market general index index was up 3.17 percent, with the country's troubled banks gaining 10.2 percent.
"He's a clear policy thinker. He was never involved in politics. He knows what needs to be done," said Thanos Papasavvas, head of currency management at Investec Asset Management in London.
But in a sign of the daunting problems any new prime minister will face, the statistics service ELSTAT reported unemployment jumped to a record high of 18.4 percent in August -- at the height of the tourism season when the rate traditionally falls -- from 16.5 percent in July.
Papandreou and the other leaders turned up smiling for a fourth day of talks on the coalition that must secure financial aid before Greece runs out of money in a just over a month.
"This is the third time that I've come here over the same issue. I hope it will be the last," conservative leader Antonis Samaras told reporters on his way to the meeting.
BRING BACK PAPADEMOS
The collapse late on Wednesday of a deal to install the parliamentary speaker as prime minister has revived the chances of Papademos being named for the job.
The stakes are high. As well as winning parliamentary approval for the bailout, the coalition has to pass the 2012 budget and secure the latest 8 billion euro installment of Greece's original rescue that was pulled together last year, to avoid bankruptcy when big debt repayments come due in December.
Ordinary Greeks are worried that a failure to resolve the political mess will ultimately push the country to a bleaker future outside the euro zone.
Papandreou said on Wednesday he was handing over to a coalition that turned out not to exist due to the deal's collapse, and then failed to install speaker Filippos Petsalnikos, an old-style politician and personal ally, as prime minister.
On a day that was bizarre and chaotic even by Greek political standards, Papandreou wished his successor well and headed off to meet the president -- only for it to emerge that there was no successor due to feuding in the political parties.
Greeks and the nation's international lenders have watched in growing horror since Monday as party leaders fight over a shrinking list of credible candidates to lead the national unity coalition after Papandreou's government imploded.
"The politicians have succeeded in making us really angry," conservative daily Kathimerini wrote in an editorial. "The country is sinking and they are concerned with their party interests, their personal aspirations and their usual intrigues."
Greece will run out of money next month unless the new government agrees emergency funding with the European Union and International Monetary Fund, Greece's last remaining lenders.
"The country cannot afford to be in a limbo. This pending issue has to be wrapped up today," center-left Ta Nea said. "Politics cannot be a theatrical stage. Especially during a time of national crisis."
Papademos, who oversaw the country's efforts to enter the euro zone, has insisted that both the socialist and conservative parties sign written undertakings to support Greece's 130 billion euro bailout, as demanded by the European Union, a government source said.
Papandreou gave an emotional television address on Wednesday, supposed to be his last to the nation as prime minister, saying the apparent deal on the speaker had saved the country's membership of the euro zone.
"I am proud that, despite the difficulties, we avoided bankruptcy and ensured the country stayed on its feet," he said. "I want to wish the new prime minister success, I will support the new effort with all my strength.
Papandreou and Samaras then began talks with President Karolos Papoulias on the new coalition.
However, before leaders of smaller parties could join them to seal the coalition, the meeting was abruptly halted, with large sections of Papandreou's PASOK party and the conservative New Democracy refusing to back Petsalnikos.
For its part, the European Union needs to put out the fire in Greece to prove to international financial markets that it can tackle another blaze in Italy, a far bigger economy also in economic and political crisis.