The poll published in a newspaper showed the 'Yes' campaign slightly in the lead but well within the margin of error. It also showed an overwhelming majority -- 74 percent -- want the country to remain in Europe's joint currency, the euro, compared to 15 percent who want a national currency.

Prime Minister Alexis Tsipras called the referendum last weekend, asking Greeks to decide whether they should accept creditor reform proposals in return for vitally needed bailout funds. He is advocating a 'No' vote on Sunday. But those proposals are no longer on the table after negotiations with European creditors broke down last weekend and Greece's bailout expired on Tuesday, meaning the country no longer has access to the rescue loans.

The 'Yes' campaign says the referendum is in fact a vote on whether Greece wants to remain in the euro and in Europe. The government rejects this as scaremongering, saying a 'No' vote will put it in a better bargaining position and will not lead Greece to leave the eurozone.

The survey conducted by ALCO found 41.5 per cent will vote 'Yes' on Sunday and 40.2 percent saying they will vote 'No,' with 10.9 percent undecided. The rest said they would abstain or leave their ballots blank.

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