A man walks by fresh anti-EU graffiti in Athens, Greece June 28, 2015. Greece said it may impose capital controls and keep its banks shut on Monday after creditors refused to extend the country's bailout and savers queued to withdraw cash, taking Athens' standoff with the European Union and the International Monetary Fund to a dangerous new level. The word painted over the European Union flag reads, "No". [Photo/Agencies]

On the streets of Athens, reactions to Tsipras' referendum call were mixed.

"I have no idea what we are voting for. Yes or no, we don't know what to say," 67-year-old Triandafila Bourbourda said as she walked in the capital's main Syntagma Square. "I think we shouldn't have gone so far to get into this mess."

But Voula Lambrou, attending a Sunday morning church service, said she believed Greece would be better off outside the 28-nation EU.

"If we exit the European Union, I believe things will be very good for Greece," she said. "It will be tough for some time, but we will be able to find strength in order to carry on ahead. We don't need the Europeans."

Two opinion polls published Sunday indicated that more Greeks want to stay in the eurozone and make a deal with creditors than want a rupture with the country's European partners. Both polls were conducted before Tsipras' referendum call, but they provide an indication of public sentiment.

In the poll by Alco for the Proto Thema paper, 57 percent said they believed Greece should make a deal while 29 percent wanted a rupture of ties. A Kapa Research poll for To Vima newspaper found that 47.2 percent would vote in favor of a new, painful agreement with Greece's creditors, compared to 33 percent who would vote no and 18.4 percent undecided.

Both polls were conducted from June 24-26 and had a margin of error of about 3.1 percent.

On the banking front, the ECB has said it could reconsider its decision on credit levels.

"We continue to work closely with the Bank of Greece and we strongly endorse the commitment of member states in pledging to take action to address the fragilities of euro-area economies," ECB chief Mario Draghi said.

Yannis Stournaras, governor of the Bank of Greece, said the bank would "take all measures necessary to ensure financial stability for Greek citizens in these difficult circumstances."

David McHugh in Frankfurt, Geir Moulson in Berlin and Jamey Keaten in Paris contributed to this report.