Eurozone finance ministers say they expect to hear new proposals from Greece after the country voted to reject the terms of a bailout.
A spokesman for German Chancellor Angela Merkel said there was currently "no basis" for talks on a new bailout and the ball was in Greece's court.
Mrs Merkel is to meet French President Francois Hollande in Paris on Monday.
Germany's economy minister has warned that any unconditional debt write-off would destroy the single currency.
"I really hope that the Greek government - if it wants to enter negotiations again - will accept that the other 18 member states of the euro can't just go along with an unconditional haircut (debt write-off)," said Sigmar Gabriel, who is also Germany's vice-chancellor.
"How could we then refuse it to other member states? And what would it mean for the eurozone if we'd do it? It would blow the eurozone apart, for sure," he added.
Eurozone finance ministers are to meet on Tuesday followed by a full summit of eurozone leaders. According to a Greek government official, Prime Minister Alexis Tsipras is expected to present fresh proposals at the summit.
Mr Tsipras has noted that a recent IMF assessment confirmed that restructuring Greece's debt of more than €300bn (NZ$496) was necessary.
In another development, Greek officials named Euclid Tsakalotos to replace outspoken Finance Minister Yanis Varoufakis, who resigned yesterday.
Meanwhile, the European Central Bank (ECB) is discussing whether to raise its emergency cash support for Greek banks, which are running out of funds and on the verge of collapse.
Last week, Greece ordered banks to close after the ECB froze its financial lifeline following the breakdown of bailout talks in Brussels.
Capital controls have been imposed and people are queuing to withdraw their limit of 60 euros a day.
Greece's Economy Minister, Georgios Stathakis, told the BBC the ECB had to keep Greek banks alive for seven to 10 days so that negotiations could take place.
Global financial markets have fallen over fears that Greece is heading for an exit from the euro.
Head of the Eurogroup of finance ministers, Jeroen Dijsselbloem, said the result of Sunday's referendum was "very regrettable for the future of Greece".
"For recovery of the Greek economy, difficult measures and reforms are inevitable. We will now wait for the initiatives of the Greek authorities," he said.
Mrs Merkel's spokesman, Steffen Seibert, said Greece had to make the next move.
"It is up to Greece to make something of this. We are waiting to see which proposals the Greek government makes to its European partners," he said.
At a news conference in Brussels, the European Commission vice-president for the euro, Valdis Dombrovskis, said the Greek government needed to be "responsible and honest" with its people about the potential consequences of the decisions it was facing.
"The 'no' result, unfortunately, widens the gap between Greece and other eurozone countries," he said.
"There is no easy way out of this crisis. Too much time and too many opportunities have been lost."
But he said the stability of the eurozone was not in question, adding: "We have everything we need to manage the situation."
Hours after the referendum result, Yanis Varoufakis resigned as finance minister, saying that eurozone finance ministers, with whom he had repeatedly clashed, had wanted him removed.
Mr Varoufakis said he had been "made aware of a certain preference by some eurogroup participants, and assorted 'partners', for my... 'absence' from its meetings".
His replacement, 55-year-old economist Euclid Tsakalotos, was Mr Tsipras's lead bailout negotiator.
Greece had been locked in negotiations with its creditors for months when the Greek government unexpectedly called a referendum on the terms it was being offered.
Greece's last bailout expired on Tuesday and Greece missed a €1.6 billion (NZ$2.6 billion) payment to the IMF.
The European Commission - one of the "troika" of creditors along with the IMF and the ECB - wanted Athens to raise taxes and slash welfare spending to meet its debt obligations.
Greece's Syriza-led government, which was elected in January on an anti-austerity platform, said creditors had tried to use fear to put pressure on Greeks.