Finance Minister Yanis Varoufakis said it would be catastrophic for Greece to leave the euro
Greece cannot make a repayment to the International Monetary Fund (IMF) due on 5 June as it does not have the money, the interior minister says.
"The four instalments for the IMF in June are €1.6bn, this money will not be given and is not there to be given," Nikos Voutsis told Greek TV.
Greece has to come to a deal with the IMF and EU to secure the final tranche of its bailout from the institutions.
The finance minister meanwhile told the BBC that progress was being made.
Yanis Varoufakis said Greece had worked hard to meet its end of the deal with its lenders, and that now it was up to the international institutions to reciprocate.
"Greece has made enormous strides at reaching a deal," he told the Andrew Marr Show.
"It is now up to institutions to do their bit. We have met them three-quarters of the way, they need to meet us one-quarter of the way."
Greek Finance Minister Yanis Varoufakis
Analysis: Joe Lynam, BBC business correspondent
The Greek interior minister Nikos Voutsis is "of the far left" in a hard left-wing Syriza party but should not be disregarded as on the fringe, or irrelevant, within the government.
He is one of a number of different voices around the cabinet table with varying degrees of influence. So his comments that Greece cannot and will not pay the IMF €1.6bn next month should not be fully discounted.
There is a theory that the Prime minister Alexis Tsipras allows his ministers to let off steam in interviews in order to give him leverage when negotiating with creditors in Brussels or Berlin.
It is also true that the Greek Finance Minister Varoufakis has been sidelined by Athens. All areas of discussion with the troika (EC, ECB and IMF), must be agreed by Mr Tsipras personally.
The Greek government, EU and IMF have been locked in negotiations for four months over economic reforms the IMF and EU say must be implemented before more money is made available.
Greece's last cash injection from its international creditors was in August and the final €7.2bn instalment from its two €240bn EU-IMF bailouts is now seen as vital.
But first it has to meet the 5 June repayment deadline. If it fails to come to a deal with its partners, there is a fear it could default on its loans.
That could push the Greek government towards leaving the single currency, otherwise known as Grexit.
"It would be a disaster for everyone involved," said Mr Varoufakis
"It would be a disaster primarily for the Greek social economy, but it would also be the beginning of the end of the common currency project in Europe.
"Once you infuse into people's minds, into investors' minds, the idea that the euro is not indivisible, it will be only a matter of time before the whole thing begins to unravel."
Greece has been shut out of bond markets, and with the current deadlock Athens has been struggling to meet debt obligations and to pay public sector wages and pensions.