European Council President Herman Van Rompuy said Monday that EU leaders at the summit called for clinching a deal between Greece and its lenders on cutting its debt by the end of the week.

"We welcome the progress made in the negotiations with the private sector. We count on the Greek authorities and the (EU-IMF) troika to agree on the steps to put the current programme back on track," Van Rompuy said at a press conference after the summit.

"We urge the Greek authorities and all parties involved to finalize negotiations on the new program in the coming days. Restorations of credibility requires that all political parities irrevocably commit to the new program," Van Rompuy said.

German Chancellor Angela Merkel tried to placate critics of a German proposal to put Greece under the supervision of an EU commissar, saying Europe must help Greece enact economic reforms.

Asked on the German proposal, Merkel told journalists at Monday's EU summit that the debate must be on "how Europe can help Greece accomplish the tasks given to it."

"One must find ways through more action from the Greek government, through more contributions from private creditors, for example, to close this gap," Merkel said. "That is being negotiated now."

German officials last week proposed the idea of appointing a European "budget commissioner" by the 16 other eurozone finance ministers that could veto budget decisions made by Athens.

Greece rejected the proposal outright, with Greek Finance Minister Evangelos Venizelos saying on Sunday that "bigger nations" shouldn't force Greece to confront a "dilemma of 'economic assistance or national dignity.' "

However, Greece's EU partners are still waiting for the country to meet tough fiscal targets. Greece and its private creditors said Saturday that they expect to complete a deal in coming days after bondholders signaled they would accept European government demands for a bigger cut in their debt holdings.

Greek debt restructuring aims to bring its debt down to 120 percent of its gross domestic product (GDP) by 2020.

Euro zone governments agreed last year on the second bailout package of 130 billion euros (171 billion dollars) for Greece, which asked Greek private creditors to accept a 50 percent reduction in the value of their holdings of Greek debt.

Merkel had said that Greece will not receive its next batch of bailout cash unless the terms of the private sector involvement are agreed very soon.

Germany's finance minister Wolfgang Schauble warned Monday that the eurozone might refuse to grant Greece a fresh bailout, urging Greece to show that it can overhaul its economy.

"Unless Greece implements the necessary decisions and doesn't just announce them..there's no amount of money that can solve the problem," Schauble said in an interview with The Wall Street Journal.