Without the contingency package, lenders refuse to disburse new loans or discuss debt relief for Greece. Without new loans, Athens will be forced to go into arrears with domestic payments.
Greece also faces a total of about 5 billion euros in debt repayments until the middle of July.
"We have to avoid a situation of renewed uncertainty for Greece. Therefore we need a specific date for the new Eurogroup meeting in the not-distant future, and I am not talking about weeks but about days," Tusk said.
He said he had consulted closely on Greece with the head of the Eurogroup, Jeroen Dijsselbloem, and the president of the European Commission, Jean-Claude Juncker.
Greece's benchmark stock market fell sharply on Wednesday, underperforming other European markets, after news of the delayed meeting.
Greece's benchmark ATG equity index fell 4.4 percent, underperforming a 0.2 percent decline on the broader, pan-European STOXX 600 index. Shares in major Greek banks also declined sharply, with Eurobank Ergasias down 14 percent, while Alpha Bank fell 8 percent.
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