Prime Minister Alexis Tsipras admitted his country was unlikely to meet the debt.
“How is it possible the creditors are waiting for the IMF payment while our banks are being suffocated?” he said in an interview on Greek TV.
Athens withdrew from negotiations over a new EU bailout package at the weekend after it was made clear it would have to impose austerity measures in exchange for cash, Sky News reports.
Mr Tsipras instead arranged a referendum for Sunday – and is urging voters to say no to the bailout proposal.
European leaders have warned this would lead to Greece leaving the monetary union.
French president Francois Hollande said: “What is at stake is whether or not Greeks want to stay in the eurozone or want to take the risk of leaving.”
German Vice-Chancellor Sigmar Gabriel added: “It must be crystal clear what is at stake. At the core, it is a yes or no to remaining in the eurozone.”
Mr Tsipras asked for Greece’s bailout programme, which expires today, be extended for a month to allow the referendum to be carried out “in a calm and positive climate”.
However, eurozone leaders immediately rejected the idea.
But despite their rhetoric, Mr Tsipras does not believe they will allow Greece to crash out of the eurozone.
“I don’t believe they want to throw us out of the euro or that they will,” he said. “They won’t do this.
“Let me explain why: because the cost is massive.
“The financial cost of breaking up the euro, the start of the break-up, the cost of a bankruptcy of one country which has an ECB (European Central Bank) exposure of more than €120bn, is massive. It won’t happen, that’s my estimation.”
Tsipras’ hand has been strengthened after 17,000 people took the streets in Athens and Thessaloniki to protest against the latest bailout proposals.
As the financial crisis deepens, banks and the country’s stock exchange are remaining shut until 7 July, and the daily limit on withdrawals from cash machines has been cut to just €60.
Concerned British tourists who are heading to Greece have been told the ATM limits will not apply to foreign debit cards – but in practice, some cash machines may not be able to tell the difference.
The Association of British Travel Agents is advising visitors to take all of the euros they may need in cash, but says credit and debit card transactions in shops and restaurants will be unaffected.
Meanwhile, European stock markets have fallen sharply as nervous investors fear the ramifications of a Greek debt default, with the euro weakening further against the pound and dollar.