Interior Minister Nikos Voutsis made his comments during a weekend TV programme.
Stocks on Greece's ATG index closed 3.11% lower at 814.06.
Greece still needs to strike a deal with its creditors in order to release €7.2bn (£5.1bn) in remaining assistance.
"The four instalments for the IMF in June are €1.6bn, this money will not be given and is not there to be given," Mr Voutsis said.
The country's finance minister meanwhile has told the BBC on Sunday that progress was being made.
"Greece has made enormous strides at reaching a deal," Yanis Varoufakis told the Andrew Marr Show.
Other benchmark indexes across Europe have also fallen.
The IBEX closed down 2.01% to 11,322.3 after Spain's voters punished the ruling Popular Party (PP) in local and regional elections.
"Sunday's losses by the ruling party are seen as a protest against the country's economic hardship, which is shown most clearly in an unemployment rate of 23% - and more than double that among young people," said BBC economics correspondent Andrew Walker.
Financial markets were unsettled by the vote against an economic strategy that many investors broadly support, he added.
France's Cac-40 closed down 0.5% to 5117.1, and Italy's MIB closed down 1.94% to 23,305.
Stock markets in London and Germany were closed for public holidays.

The drugs, worth an estimated £831,000, were found in a factory near Bridgend's main custody suite in November.
Christopher Bennett, 61, of Port Talbot, Dale Hart, 53, of Pencoed, and Michael Smart, 37, of Pencoed were bailed until 29 April.
They will appear at Cardiff Crown Court.
Mr Smart also faces a second charge of possessing cocaine.

The International Telecommunication Union (ITU), a United Nations body, predicts that 3.2 billion people will be online. The population currently stands at 7.2 billion.
About 2 billion of those will be in the developing world, the report added.
But just 89 million will be in countries such as Somalia and Nepal.
These are part of a group of nations described as "least developed countries" by the United Nations, with a combined population of 940 million.
There will also be more than 7 billion mobile device subscriptions, the ITU said.
It found that 78 out of 100 people in the US and Europe already use mobile broadband, and 69% of the world has 3G coverage - but only 29% of rural areas are served.
Africa lags behind with just 17.4% mobile broadband penetration.
By the end of the year 80% of households in developed countries and 34% of those in developing countries will have internet access in some form, the report continued.
The study focused on the growth of the Information and Communication Technology (ICT) sector over the past 15 years.
In the year 2000 there were just 400 million internet users worldwide, it said - an eighth of the current figure.
"Over the past 15 years the ICT revolution has driven global development in an unprecedented way," said Brahima Sanou, director of the ITU telecommunication development bureau.
"ICTs will play an even more significant role in the post 2015 development agenda and in achieving future sustainable development goals as the world moves faster and faster towards a digital society."
European stocks have fallen after a Greek minister said that Athens would struggle to meet its upcoming debt payments.
[NEXT_CONCEPT]
Three men appeared in court jointly charged with producing 692 cannabis plants - yards from South Wales Police's headquarters.
[NEXT_CONCEPT]
Nearly half of the global population will be using the internet by the end of this year, according to a new report.