Eurozone finance ministers holding a crisis meeting in Luxembourg pressed Athens to finally present a credible reform plan and end the five-month standoff between Greece's anti-austerity government and its creditors.
But with Athens owing a 1.6-billion-euro payment to the IMF at the end of June and Greece's international bailout due to expire the same day, they were pessimistic about the chances of a deal today.
"There will be no period of grace" for the loan payment, Lagarde told reporters before she joined the ministers for their Eurogroup meeting. "I have a term of June 30 - if it's not paid by July 1, it's not paid."
Europe's most powerful leader, German Chancellor Angela Merkel, weighed in on the issue earlier today when she told German lawmakers in the Bundestag she was "still confident" that a deal was possible.
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But the mood was darker in an overcast Luxembourg, where ministers were openly broaching scenarios such as a Greek exit from the euro if it defaults on its debts.
"The next step to make the deal credible, also financially sustainable, will have to come from the Greek side," the Dutch Eurogroup chief Jeroen Dijsselbloem told reporters.
No deal at the Eurogroup meeting means the issue will likely go to the wire at an EU leaders' summit in Brussels on June 25 and 26.
Greek Finance Minister Yanis Varoufakis, the motorbike-riding former economist whose relations with his counterparts have been strained, said he wanted to "replace costly discord with effective consensus."
"Today we are going to be presenting the Greek government ideas," he added, without specifying whether he meant a new reform plan.
Without the bailout tranche and the IMF deadline missed, Greece would be for the first time in five years financially alone, with its coffers empty and all eyes on what happens next.