ATHENS—Greece said Sunday that it won't have the money it is due to repay to the International Monetary Fund next month unless it strikes a deal with international creditors over further rescue funding.

Interior Minister Nikos Voutsis told privately owned television station Mega that Greece is scheduled to repay €1.6 billion ($1.76 billion) to the IMF between June 5-19, but the payments cannot be met.

"This money will not be given," he said. "It does not exist."

Despite months of negotiations between Greece's leftist-led government and creditors—the European Union and the IMF—over the country's bailout, little progress has been made.

The ruling Syriza party, elected on an antiausterity ticket in January, opposes reforms to the labor market and pension system demanded by international creditors that argue that Greece must complete these economic overhauls to achieve sustainable growth and solvency.

A default on Greece's obligations to the IMF could spark heavy deposit withdrawals from Greek banks and force capital controls, deepening the country's economic crisis, economists say.

Talks are continuing between the two sides in Brussels, though hopes have been dashed that a recent reshuffle of Greece's renegotiating team will accelerate a deal.

The reshuffle effectively sidelined Finance Minister Yanis Varoufakis, whose combative style has alienated many European officials. In his latest comments, Mr. Varoufakis told the New York Times Magazine last week that he had secretly taped negotiations with his European peers in April, a breach of etiquette that raised eyebrows around Europe.

On Sunday, Mr. Varoufakis said that he often records his interventions and comments on his mobile phone to better brief Prime Minister Alexis Tsipras and the Greek cabinet, as was the case at the April meeting in Riga, Latvia. Mr. Varoufakis added that despite the press incorrectly reporting that he was insulted by his peers at the Latvia meeting and that he had lost his temper, he refused to leak any recording to the press that would have set the record straight.

"Perhaps we should query European institutions in which decisions of monumental importance are made, on behalf of Europe's citizenry, but in which minutes are neither taken nor published," he wrote on his personal blog.

"Secrecy and a gullible press do not augur well for Europe's democracy," he added.

Write to Stelios Bouras at stelios.bouras@wsj.com

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