Athens already had a close shave in May, when it was only able to scrape together the 750 million euros (USD 845 million) due to the IMF then by raiding its emergency reserves.
With the clock ticking down to four more debt instalments from June 5, Interior Minister Nikos Voutsis told Mega TV that the country has nothing left for the IMF in its coffers.
Nevertheless, the minister believes that negotiations between Athens and its creditors were taking place "on the basis of cautious optimism that there will be a strong agreement".
Greece's radical-left government has been locked in negotiations with its creditors -- the IMF, the European Union and the European Central Bank -- for the past four months in a bid to unlock some 7.2 billion euros in bailout cash.
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But with a punishing debt repayment schedule in the next three months, the country now desperately needs the rescue funds.
In addition, the government has running costs to meet, including salaries to civil servants and pensions.
Last week, the parliamentary spokesman for Syriza said that the government would be unable to honour a repayment to the IMF on June 5 as its priority is to pay salaries, pensions and running costs.