Updated at 6:46 p.m. ET
European leaders warn that only five days remain to strike a deal with Greece, even as Prime Minister Alexis Tsipras says his talks with them Tuesday "took place in a positive climate."
Eurozone leaders had given Greece until Thursday to come up with a detailed plan after Tsipras showed up without one at a meeting in Brussels Tuesday. The meeting came just two days after Greeks rejected their creditors' conditions for a fresh installment of bailout money. European leaders warned that a failure to strike a deal by Sunday could mean a Greek exit from the eurozone.
A joint statement by eurozone leaders late Tuesday night said the heads of the eurozone countries will meet Sunday to discuss the Greek proposals.
European Council President Donald Tusk called on all sides to "find consensus," noting that "we have only five days left to find the ultimate agreement."
"If this does not happen, it will mean the end of the negotiations with all the possible consequences, including the worst-case scenario, where all of us will lose," Tusk said. "Our inability to find agreement may lead to the bankruptcy of Greece and the insolvency of its banking system. And for sure, it will be most painful for the Greek people."
He added: "Until now, I have avoided talking about deadlines. But tonight I have to say loud and clear that the final deadline ends this week."
Tsipras told reporters Greece's proposals contain "credible reforms that are socially just and include in reciprocity a commitment to cover the country's financial needs in the medium term, a strong investment package to counter big problems such as unemployment, as well as the start of substantial talks and the restructuring of debt."
The translation of his comments in Greek was provided by The Associated Press, which noted that Tsipras did not specify whether the proposals were verbal or written.
Tsipras he hoped to reach an agreement by "the end of the week at the latest."
Earlier, European leaders called on Greece to issue "serious and credible proposals" to try to find a way forward. The German and French leaders issued the call ahead of a meeting of eurozone leaders on Tuesday.
The Guardian reports:
" 'We are now waiting for precise proposals from the Greek prime minister, for a [program] that will allow Greece to return to prosperity. It is urgent to have these proposals so we can find a way out of this situation,' said the German chancellor, Angela Merkel, after talks with her counterpart, the French president, François Hollande.
"Expectations of a breakthrough at the high-level talks on Tuesday night were dampened by the president of the European commission, Jean-Claude Juncker. Speaking at the European parliament on Tuesday morning, he said a solution would not appear overnight. 'What we are going to do today is to talk to each other and restore order,' he said."
Finance ministers said they needed concrete proposals from Greece to figure out what's next.
At issue here is whether Greece will use the referendum as leverage to get more favorable terms from the EU. Greece, for example, could demand that the EU erase part of its debt.
The Guardian reports that Slovakia's finance minister, Peter Kazimir, said that is his country's red line.
"For my country nominal debt relief is impossible," Kazimir said as he arrived for the meeting.
On the other hand, Pierre Gramegna of Luxembourg, which currently holds the EU presidency, left the door open to looking at debt relief, saying, "Everything must be discussed."