On Tuesday, Greece failed to meet the payment deadline to the International Monetary Fund (IMF) which was the first such failure by a developed country. Earlier, negotiations between Greece and its creditors on a modified reform program in exchange for additional funding from the European Union also failed to yield a result.
The poll shows that support for the "No" vote had been much higher, at about 57 percent, before Greek authorities imposed capital controls and closed the banks on Monday, allowing only a maximum withdrawal of 60-euro in cash per day.
The collated data also showed support for the "Yes" vote climbing from 30 to 37 percent.
Greece's overall debt to international creditors stands at about $350 billion, of which $270 billion is owed to the European Central Bank (ECB), the International Monetary Fund (IMF) and eurozone countries.