Eurozone leaders will meet for an emergency summit Tuesday on Greece, at which Greek Prime Minister Alexis Tsipras is expected to offer new proposals for resolving his country's debt crisis.
Germany has warned that Athens faces being ejected from the eurozone unless it makes deeper concessions, but the Greek people voted resoundingly Sunday against further austerity measures.
As the stakes grow for Greece by the hour, the lines at ATM machines build through the night. With the banks close to collapse, the country is on the precipice of a euro exit.
Greek government controls on withdrawals have been extended through Wednesday, with some analysts saying that without a new bailout agreement, the banks could run out of money within days.
Tsipras spoke Monday by phone with German Chancellor Angela Merkel, Europe's chief advocate for imposing tough austerity measures on the Athens government.
Their conversation took place in the aftermath of a resounding Greek vote Sunday against the lenders' demand for new financial restrictions in Greece in exchange for more bailout money to keep its banks from running out of money.
Later, the German leader met with French President Francois Hollande in Paris about the Greek crisis, and they declared that the door is open for more negotiations with Athens.
But European officials did not immediately change their stance against easing terms of a possible new bailout in the wake of the 61 percent vote against more austerity.
Economic analysts say the long-running dispute could still force Greece from the 19-nation euro currency bloc, which would make it the first country to exit the eurozone in its 16-year history.
In Washington, White House spokesman Josh Earnest said it is in "the collective interests" of Europe and the United States that Greece reaches a new bailout deal with its lenders, with Athens agreeing to "a package of reforms."
U.S. stock prices moved down, but the declines were not as large as some analysts predicted. Most markets around the world, including those in Europe, fell because of the financial uncertainty created by the Greek vote.
Debate around possible Grexit
The chief of the eurozone's finance ministers, Dutch Finance Minister Jeroen Dijsselbloem, said keeping Greece in the eurozone "is still their objective and mine;" but he said the referendum "doesn't bring us closer to a solution right away.
"I have to say again that whatever the result of the referendum, tough measures are necessary in Greece, otherwise the country won't recover, otherwise the government won't work better, otherwise the economy won't start turning," he said. "And if the government and population reject difficult measures, then we get to a very difficult place, especially for the Greek people."
A leading German economist predicted a likely Grexit, or Greek exit, from the eurozone. "I have very little hope that Grexit can be avoided," said Henrik Enderlein. He said there is an 80 percent probability the Grexit will happen. "This situation is extremely dangerous for the euro area."
"The ball is now in Greece's court," Finnish Finance Minister Alexander Stubb said. "Negotiations can only be resumed when the Greek government is willing to cooperate and commit itself to measures to stabilize the country's public economy and implement the structural reforms required for debt sustainability."
Other European reactions
Meanwhile, the French finance minister held out the possibility of further talks with Greece. Michel Sapin said discussions with Greece are not "taboo," but added Greece has no hope of recovering from its financial chaos "in the months and years to come" with its current repayment obligations.
"Europe is facing a difficult moment, but it is not in difficulty itself," Sapin said. "Europe will show it is strong by protecting itself."
French European Affairs Minister Harlem Desir said the Greek "no" vote Sunday in the snap referendum did not mean Greece wants to leave the euro, but talks with Greece must start soon "on a serious basis."
The European Commission said it "respects" the result of the referendum.
The credit ratings agency Fitch said the "no" vote in the referendum "dramatically increases" the risk that Greece will leave the currency bloc.
Greek Finance Minister Yanis Varoufakis resigned Monday, a surprise because he had said he would only step aside if his fellow citizens voted in favor of accepting the austerity demands.
Varoufakis, however, said Monday he was "made aware of a certain preference" by some members of the eurozone for his "absence" from meetings of finance ministers. He said his withdrawal from such meetings was "an idea the prime minister judged to be potentially helpful to him in reaching an agreement" with Greece's creditors.
Varoufakis has often clashed with the international lenders in the past few months. And a few days ago, he accused the European Union of "terrorism" by trying to scare the Greeks into voting the way EU leaders wanted, in favor of more austerity.
On Monday, Varoufakis said, "I shall wear the creditors' loathing with pride."
Greece named its lead bailout negotiator, Euclid Tsakalotos, as its new finance minister.
Prime Minister Tsipras, who had urged a "no" vote, said after the outcome, "Today we celebrate the victory of democracy." He said the public mandate will give him a stronger hand to reach a better deal with Greece's creditors. The prime minister said voters had made "a very brave choice."
Greek opposition leader Antonis Samaras announced his resignation, after his New Democracy party had urged a 'yes' vote.
Whether the creditors will eventually pull back austerity demands and approve more bailout money for Greece is far from certain. As Athens defaulted on a $1.8 billion loan payment due the IMF last week, European leaders said a negative vote would signal that Greece wants to leave the eurozone and divorce itself politically from Europe.
Thousands of Greeks gathered in Athens' main square Sunday night to cheer the outcome of the referendum, with many chanting, "No, no!"
Nearly 10 million people were registered to vote in the referendum, with officials saying more than more 62 percent actually voted.
Running out of cash
The week leading up to Sunday's referendum was miserable for most Greeks.
The government put strict limits on withdrawals — 60 euros a day ($67) — although many ATMs quickly ran out of cash. Supermarkets are fast running out of basic foods. Storekeepers are reluctant to restock shelves because of the uncertainty of how they would be able to pay for the supplies.
European leaders have accused Athens of refusing to make any more economic reforms, while the Greeks say they have sacrificed enough and feel enslaved to their creditors.
WATCH: Related video report by Henry Ridgwell in Athens: