Tsipras is set to offer a new plan of economic measures to creditors that he hopes will restart negotiations on getting new loans for his country. The situation is urgent — without a deal, Greece's banks could go bust within days, the first step in the country's potential exit from the euro currency union.
Greece's financial distress became more acute late Monday when the European Central Bank refused to increase assistance for Greek banks, which are not due to reopen until Thursday.
A hastily arranged meeting of eurozone finance ministers, which will be Euclid Tsakalotos' first as Greek finance minister, is slated for the afternoon in Brussels. A full summit of leaders will then follow.
European officials were cautious about the prospects for progress.
Jean-Claude Juncker, the president of the European Union's executive Commission, indicated a comprehensive deal for Greece was unlikely to be reached Tuesday.
"Were we to come up with a solution today, it would be an overly simplistic solution," he told European lawmakers ahead of the meetings. "What we're going to do today is talk to each other, understand each other, show tolerance to each other and restore order to the situation."
The eurozone's top official, Jeroen Dijsselbloem, said that the pressure was on Greece to present an acceptable deal, since its position was increasingly dire financially.
"The Greek government has a major interest in coming forward quickly with serious and credible proposals," said Dijsselbloem, who is the Dutch finance minister and chairs meetings with his eurozone counterparts.
The upcoming talks follow Tsipras' bigger-than-expected win in Sunday's bailout referendum, when 61 percent of Greek voters rejected measures creditors had proposed last week in exchange for loans.
In a sign he may be willing to compromise, Tsipras appointed a new finance minister to lead talks with creditors.
Tsakalotos, a 55-year-old economist, has replaced Yanis Varoufakis, who constantly clashed with his peers.
"I won't hide from you that I am very nervous and very anxious," Tsakalotos said after being sworn in Monday. "I am not taking over at the easiest moment in Greek history."
Greek banks are running out of cash even after the government shut them last week and placed limits on how much depositors can withdraw or transfer.
Normal commerce is now impossible in Greece. Small businesses, lacking use of credit cards or money from bank accounts, were left to rely on cash coming from diminishing purchases from customers. But Greeks are holding tightly onto what they have. And suppliers are demanding that businesses pay cash up front.
Giorgos Kafkaris, a 77-year-old pensioner, was among Greeks standing in line to withdraw cash at an Athens ATM on Tuesday.
"I came to get the 120 euros, I can't take more. The good thing is we had sorted things out earlier and we had 200-300 euros set aside," he said. "I'm waiting for something better for all of us. I believe something better will happen."
The euro was down 0.7 percent ahead of Tuesday's meetings, though stock markets were relatively stable in Europe. Greece's stock market remains closed since last week amid the bank closures.
Tsipras has previously indicated he's willing to raise taxes and cut some spending provided the country gets some debt relief.
European officials are split on the issue of whether to grant Greece easier debt repayment terms — with lead eurozone lender Germany still reluctant.
Greece has been granted two bailout programs worth a total of 240 billion euros ($266 billion) in loans from other eurozone countries and the International Monetary Fund. But the spending cuts and tax increases demanded as a condition for the loans have hit growth, causing an economic depression and pushing unemployment to 25 percent. The government, meanwhile, has been slower than hoped in making the economy more competitive and selling state assets to raise money.
James Nixon, chief European economist at Oxford Economics, said there's "a narrow trajectory from here that sees an emboldened Greek parliament accepting the need for reform in return for a debt write-down."
"The next 48 hours will be crucial."
Costas Kantouris in Athens contributed to this report.
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