Greek Premier Alexis Tsipras is to present proposals at a eurozone meeting on Tuesday aimed at restarting talks with creditors after voters rejected their earlier proposals.
But German Chancellor Angela Merkel said Monday that the conditions for opening new negotiations with Greece "are not there yet".
Following a meeting with French President Francois Hollande, she added that "precise proposals" from Greece would be welcome, adding that the "door remains open".
Hollande said that "the door is open to negotiations" with Greece if Tsipras "makes serious and credible proposals" on resolving its debt crisis. Eurogroup finance ministers are holding an emergency meeting on the issue early afternoon Tuesday and Germany warned Monday morning that Berlin saw little scope for fresh negotiations with Greece after Sunday's No vote in a national referendum on creditors' proposals.
"Given the referendum result, at the moment the prerequisites don't exist for new negotiations on other aid programmes," spokesman Steffen Seibert said.
Similar sentiments were heard from the International Monetary Fund. IMF Managing Director Christine Lagarde said the agency is "closely monitoring the situation and is ready to help if Athens asks".
However, a restructuring of Greek debt "is not on the table," European Commission Vice President Valdis Dombrovskis said.
Such a move was impossible because Greece had not successfully completed the European Financial Stability Facility (EFSF) programme, he added.
Tuesday's eurozone meeting and other talks in European capitals will have to indicate "a definitive way to resolve" the Greece debt crisis, Premier Matteo Renzi said.
Meanwhile, Greek banks said they would remain closed until Wednesday and continued to limit the amount the public could withdraw amid rising fears about how long the country could continue financially.
Late Monday, the European Central Bank (ECB) said it would continue to provide support to the banking system in Greece by maintaining its Emergency Liquidity Assistance program there.
Meanwhile Euclid Tsakalotos, head of the Greece debt negotiating team, was named new finance minister in place of Yanis Varoufakis who quit Monday.
The removal of Varoufakis, who alienated some when he accused Greece's creditors of "terrorism", may help to facilitate fresh negotiations to avert a Greek default and an exit from the eurozone.
Germany shrugged off the change.
"The question is not about the people, but about the (negotiating) positions," said Seibert.
At the same time the eurozone's top official said he still wants Greece to stay in the single European currency.
The Greeks also want to keep using the euro, added Eurogroup President Jeroen Dijsselbloem.
"That is their goal, and still mine," he said.
"We are going to see in the coming days if there are still openings. But there are no easy solutions".
Dijsselbloem added that tough measures were still necessary in Greece. "And if the government and population reject tough measures, then we get to a very difficult place," he said.
The uncertainty hit financial markets hard on Monday.
Italy's FTSE Mib shed 4.03%.
Despite the turmoil, Dombrovskis said that "the stability of the eurozone is not in question".
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