BRUSSELS — Frustrated European leaders gave Greece until Sunday to reach an agreement to save its collapsing economy from catastrophe after an emergency summit meeting here on Tuesday ended without the Athens government offering a substantive new proposal to resolve its debt crisis.

“The situation is really critical and unfortunately we can’t exclude the black scenarios of no agreement,” said Donald Tusk, the president of the European Council, warning that those possibilities included “the bankruptcy of Greece and the insolvency of its banking system” and great pain for the Greek people. Also looming ever larger was the prospect of Greece leaving the European currency union.

Mr. Tusk said that the government of Prime Minister Alexis Tsipras had until Thursday to deliver a new plan to Greece’s creditors.

“Until now I have avoided talking about deadlines,” Mr. Tusk, a former prime minister of Poland, told reporters after a day of fruitless meetings. “But tonight I have to say it loud and clear — the final deadline ends this week.”