Alexis Tsipras calls referendum ‘day of celebration’, in which almost 10 million Greeks have right to vote on whether nation should accept its creditors’ terms

Greeks have begun voting in a referendum that presents the biggest challenge to the euro since its adoption, and risks sending shockwaves through the world’s financial markets.

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Casting his ballot in the central Athens district of Kypseli, the country’s prime minister, Alexis Tsipras, called the referendum a “day of celebration”. Addressing a crush of reporters as loud cries of “no” rang out from supporters, Tsipras lashed out at the propaganda war waged in the week since he called the vote.

“Democracy has defeated fear. The determination of the people will beat the propaganda of fear,” he said, in an apparent reference to warnings from the opposition and European leaders that a no vote could lead to Greece’s exit from the euro and even the EU. Tsipras, who along with his leftwing Syriza party has campaigned for Greeks to vote no, added: “The people are sending a message. A government can be ignored but no one can ignore the desire of an entire people to take life in its hands.”

The conservative opposition leader, Antonis Samaras, also cast his ballot, saying: “We vote yes to Greece. We vote yes to Europe.”

The referendum comes at the end of a week of unending drama during which Greece closed its banks, rationed cash, failed to repay the IMF and lost billions of euros when its bailout programme expired. The vote is on the last terms offered to Greece before Tsipras abandoned talks with his country’s lenders last weekend, saying their conditions would only exacerbate the plight of a country whose economy has already shrunk by a quarter.

The Greek president, Prokopis Pavlopoulos, emphasised the need for national unity as voting got under way. It is only the second referendum to take place in more than 40 years, and takes place as signs of social division and fears of civil strife increase.

“Irrespective of the result, we have to traverse what will be a difficult tomorrow with unity,” Pavlopoulos told reporters. “That is what our forefathers did. That is what we are going to do. We will go forward, all together.”

At a rally in the centre of Athens on Friday night, Tsipras had urged his compatriots to cast a no ballot, assuring them it would not be a vote for leaving the euro, but for remaining in Europe with dignity.

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Almost 9.9 million Greeks have the right to vote in the referendum. Nearly 110,000 who have just turned 18 will vote for the first time, according to authorities. Of that number 55,206 are men and 53,165 women. Most young Greeks, who have been hit particularly hard unemployment, are expected to vote no, pollsters say.

Among the many imponderables was the impact of votes cast by Greeks living abroad. Under the same rules that govern elections, expatriates must return to the country to take part. There was evidence that large numbers of expatriates were coming back for the referendum and that most leaned towards voting yes.

The prime minister’s decision to call the vote prompted outrage among opposition politicians. They have argued that the offer on which the referendum is based was withdrawn when the bailout programme ran out and that Syriza has rigged the ballot by putting both options on one ballot sheet with the no option first. Greece’s highest court threw out a claim that the vote was unconstitutional on Friday.

Polling stations opened at 7am local time and will close at 7pm (1700 BST). The first results are expected around 9pm.

Opinion polls have been contradictory and none has shown a clear majority for either option, but they have all shown that an overwhelming majority of Greeks, around three-quarters, want their country to keep the euro.

Both the parties in government and the neo-Nazi Golden Dawn support a no vote. The centre-right opposition New Democracy party has campaigned for a yes vote as have the centre-left Pasok and To Potami parties.

In a surprise development on the eve of polling, the German finance minister, Wolfgang Schäuble, until even more hardline towards Greece than his chancellor, Angela Merkel, adopted a more conciliatory tone.

Having previously insisted that a no vote would see the country forced out of the euro, he told the Bild newspaper that the choice was between holding on to the euro and being “temporarily without it”. It was far from clear what Schäuble had in mind, but economists have mooted the notion of a period in which Greece might go back to its national currency, the drachma, while its economy recovered.

With pharmacists in Athens reporting that the government had rationed the distribution of drugs, and fears being raised of food shortages within weeks, the finance minister of Europe’s biggest economy said: “It is clear that we will not leave the [Greek] people in the lurch.” His last-minute intervention appeared to favour the no camp’s argument that the vote is not on membership of the euro.

Schäuble’s tone was strikingly at odds with that of his charismatic but controversial Greek counterpart, Yanis Varoufakis, who turned up the heat before the ballot by accusing Greece’s creditors of terrorism.

“Why did they force us to close the banks?” he asked in an interview published by the Spanish daily El Mundo. “To instil fear in people. And spreading fear is called terrorism.”

Rallies in support of Greece were held in several European capitals on Saturday. In Britain they took place in London, Liverpool and Edinburgh.

• This article was amended on 4 August 2015. Because of an editing error, an earlier version omitted the words “numbers of”.