Updated at 10:30 a.m. ET
European creditors were still trying to forge a new deal with Athens to ward off a collapse of the Greek economy — the third bailout since 2010.
But European Union President Donald Tusk cancelled a meeting of 28 leaders, something NPR's Soraya Sarhaddi Nelson says is "a very rare occurrence which ... highlights how far the sides are still apart but also suggests there won't be a Grexit worked out, at least not today."
Tusk, she says, has vowed that the smaller Eurozone leaders' meeting, which begins at 10 a.m. EDT, will last until they conclude their talks on Greece.
German Chancellor Angela Merkel said that as frayed as nerves had become that there won't be an agreement just for the sake of unity.
"The most important currency has been lost and that's trust and reliability," she said.
Athens faces an uphill battle in convincing its creditors that this time it can be trusted to deliver on the same reform promises it has failed to push through i the past. Those changes would be in exchange for a financial rescue package securing the country's future in the euro.
The Associated Press writes: "Facing a self-imposed Sunday deadline, the European nations using the shared euro currency were still seeking more proof from Greek Prime Minister Alexis Tsipras that he could be fully trusted to enact wide-ranging economic reforms to safeguard Greece's future in the common currency."
Greece has asked for 53.5 billion euros ($59.5 billion) over three years, but the AP quotes officials in Brussels, where the talks are being held, as saying that figure will need to be much higher.
Meanwhile, Greeks citizens are keeping a nervous eye on talks that will decide their country's future, NPR's Eleanor Beardsley reports.
At the seaside town of Kiato, about an hour from Athens, thoughts are about the tough negotiations in Brussels.
One woman tells Eleanor that she can hardly watch television anymore.
"Greek TV is like a terrorist attack," the woman says. "We are all afraid to go out or talk about all this."