Greece's debt crisis sent shivers through American stock markets Monday, a day after Greek voters rejected demands from international creditors for further austerity measures in exchange for a bailout of its bankrupt economy.

The Dow Jones Industrial Average fell more than 100 points after the opening bell, at one point hitting its lowest level since early February, before recovering much of the losses, dipping below 45 points at 12 p.m. EST. The dip followed plunges by markets in Europe and around the world as the government of Prime Minister Alexis Tsipras struggled to find its way through the crisis, which included the resignation Monday morning of Finance Minister Yanis Varoufakis.

"The people there need help, and we shouldn't deny it to them just because we're not satisfied with the outcome of the referendum."

- Sigmar Gabriel, German economy minister

Greece and its membership in Europe's joint currency faced an uncertain future, with the country under pressure to reach a bailout deal with creditors. Tsipras has two days to resolve the standoff with creditors before ATMs run out of cash and civil unrest breaks out, hedge fund Balyasny Asset Management said. But making a deal will be daunting after some 61 percent of voters rejected the austerity measures lenders were demanding.

The European Central Bank said Monday it's keeping the level of emergency credit to Greek banks unchanged. That leaves the banks under increasing pressure as they try to cope with cash withdrawals and replenish cash machines in the coming days. The ECB says it is monitoring the situation in the financial markets closely and is ready to use all available measures to keep stability in the 19-nation eurozone.

“I don’t see a good resolution any time soon,” Colin Lancaster, senior managing director with Balyasny, a $9 billion fund based in Chicago, told Bloomberg News in an e-mailed statement. “The big question is whether the EU adopts a strategy of waiting them out. The hope would be that the unrest leads to a unity government or change in government.”

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Varoufakis, who applauded the vote result, said in a statement that Tsipras believes Varoufakis' resignation "might help achieve a deal" and that was what prompted him to step down.

The vote was painted by opposition parties and many European officials as one on whether Greece should remain in Europe's joint currency. In the aftermath, many officials softened their tone and said talks would resume, though Greece's chance of staying in the euro was looking increasingly shaky. Much of the world was focused on containing the contagion that could spread as a result of a member of the eurozone defaulting on its crippling debt.

Stock markets and oil prices fell in other parts of the world Monday. In Europe, the main German and French indices fell roughly 1.5 percent, while Great Britain's FTSE dropped half a percent. The declines were not as steep as feared in some quarters, and there was little evidence Greece's troubles might affect other eurozone countries imminently, with government borrowing rates for Italy and Spain rising only marginally.

White House spokesman Josh Earnest said the Greek financial crisis has not had a huge impact on the U.S. economy so far. 

"What we have seen so far is that the markets have been orderly and that spillover has been pretty limited. But again we're going to continue to encourage all of parties to pursue a solution that we believe is in their collective interest," Earnest told reporters Monday. 

In Greece, citizens were feeling the squeeze as the country's banks remained shut for a sixth working day as the government tries to limit a drain of deposits despite limits on cash withdrawals at ATMs. At one Athens bank, an employee faced a crowd of elderly Greeks as he tried to distribute line positions to enter the bank to withdraw a maximum of 120 euros ($134) for the week, the Associated Press reported.

Varoufakis’ exit may ease tensions in the crisis. He is known for his brash style and fondness for frequent media appearances at the start of his tenure, when the new government was formed in January. He had visibly annoyed many of the eurozone's finance ministers during Greece's debt negotiations.

"Soon after the announcement of the referendum results, I was made aware of a certain preference by some Eurogroup participants... for my ‘absence’ from its meetings; an idea that the prime minister judged to be potentially helpful to him in reaching an agreement."

"For this reason I am leaving the Ministry of Finance today," Varoufakis wrote in a blog post, according to The Guardian.

“It is, therefore, essential that the great capital bestowed upon our government by the splendid NO vote be invested immediately into a YES to a proper resolution – to an agreement that involves debt restructuring, less austerity, redistribution in favor of the needy, and real reforms,” the post read, according to the Athenian newspaper Kathmerini.

He said the prime minister had judged it "potentially helpful to him" if Varoufakis is absent from the upcoming meetings with Greece's creditors. Varoufakis had called the voters' rejection of the proposal a "brave" move, Sky News reported.

The Greek government named Euclid Tsakalotos, 55, as the country's new finance minister. Tsakalotos was Tsipras' lead bailout negotiator in talks that halted last month before Tsipras called a bailout referendum. He is expected to participate in an emergency meeting with creditors in Brussels Tuesday. 

Tsipras was elected on promises to repeal the austerity demanded in return for a bailout from other eurozone countries and the International Monetary Fund, and negotiations broke down late last month after dragging on unsuccessfully for five months.

With his high-stakes gamble to call a referendum on creditor proposals with just a week's notice, Tsipras aimed to show creditors that Greeks, whose economy has been shattered and who face spiraling unemployment and poverty, have had enough and that the austerity prescribed isn't working.

Germany's vice chancellor says Europe needs to be ready to provide humanitarian aid to Greece. Sigmar Gabriel, who is also Germany's economy minister, said there is a danger that Greece will suffer a shortage of essential goods such as medicine.

"The people there need help, and we shouldn't deny it to them just because we're not satisfied with the outcome of the referendum," Gabriel told reporters in Berlin.

Greeks say they're proud of their toughness and defiance after Sunday's landslide "no" vote against creditors' demands. George Papadokostakis, a 34-year-old coffee shop owner, says he's very happy with the referendum result. He says "something happened last night with the Greek people. ... we were in a dead-end situation (but) with the `no' vote we believe there may be something better."

Shoe store worker Nicky Zachary says "we can live with very little and we can live through difficult situations. And I think after the referendum, the Greek people are united."

"I don't know what will happen next. I would like to have an answer. But at least we are fighting," she added.

The eurozone's top official says he still wants Greece to stay in the single European currency. Jeroen Dijsselbloem -- also the Dutch finance minister -- says the Greeks want to keep using the euro.

"That is their goal, and still mine," he said on his way into a Dutch Cabinet meeting Monday in The Hague. "But we will have to see if it happens."

The Associated Press contributed to this report.