BRUSSELS — Just weeks before a crucial debt payment comes due, weekend talks between Greece and its European creditors broke down as both sides refused to soften their long-held bargaining positions.

The lack of progress increases the possibility that Greece will be forced to default on its mountain of debt, with 1.6 billion euros ($1.8 billion) owed to the International Monetary Fund on June 30.

Negotiations had intensified ahead of a meeting on Thursday of euro-area finance ministers, who must approve any deal that would end the long-running crisis. The goal is to find a way to unlock billions of euros in frozen aid payments in order to keep Greece from becoming the first country to leave the eurozone.

But in the wake of this latest disintegration in talks, an exit by Greece remains possible despite overtures by European Union leaders to keep Greece in the single currency bloc.

For months, European creditors have been pushing the leftist government in Athens to back down from some of its demands to ease the terms of its giant bailout program scheduled to expire at the end of the month. Those negotiations have been particularly focused on areas like setting the size of Greece’s primary budget surplus and overhauling the country’s pension system.

Late Sunday evening, however, negotiators called an end to two days of discussions, as Greek officials angrily claimed that the technocrats with whom they were holding discussions had no authority to negotiate any sort of deal.

“They wanted us to hit our targets by slashing pensions and increasing taxes,” said one senior member of the Greek negotiating team who spoke on the condition of anonymity because the discussions were private. “But they had no mandate to negotiate.”

Two senior members of the Greek government, Nikos Pappas, a close confidant of Prime Minister Alexis Tsipras, and Yannis Dragasakis, the deputy prime minister, traveled to Brussels for the talks. They met with senior-level European officials, none of whom had the same rank in their respective government posts.

“Despite the presence of the Greek delegation in Brussels, there was no response from the institutions for discussions to be held at the necessary level and with the required authorization that would allow a solution to issues that remain open,” Mr. Dragasakis said in a statement.

The pressure on Greece to reach an agreement is escalating. By the end of this month, it must come up with €1.2 billion in cash to make pension and salary payments to public-sector workers, according to senior finance officials in Athens.

With the central government’s coffers extremely bare, Mr. Tsipras’s government will be forced to raid state pension and municipal funds to make good on these payments, these people said, speaking on the condition of anonymity.

The failed talks could also jeopardize the European Central Bank’s support for troubled Greek banks. The president of the E.C.B., Mario Draghi, has said that he would cut off emergency aid to Greek banks if it became clear that there would be no agreement between Greece and its creditors. A crucial meeting of the central bank’s governing council will be held on Wednesday.

At the root of the disagreement was the insistence by creditors that Greece has to cut pension payments, increase value-added taxes and reform its labor system. They are pressing the government for a higher primary budget surplus, which is the amount of revenue Greece is required to hold in its coffers after expenses have been paid and before servicing its debt. The Greeks say that they can reach this fiscal target by taking less extreme measures, but they have not been able to persuade skeptical creditors in this regard.

Greek negotiators remain convinced that a deal can be reached at only the highest political level. That would require Chancellor Angela Merkel of Germany to find a way to accommodate the more cautious but powerful finance minister, Wolfgang Schäuble, in order to preserve stability in the eurozone.

After the talks ended Sunday evening, the European Commission — one of the three institutions, along with the International Monetary Fund and the European Central Bank, overseeing Greece’s giant bailout program — indicated that talks might have to go down to the wire to the end of June.

“While some progress was made, the talks did not succeed,” the European Commission said in a statement.

There remained “a significant gap” between what creditors, including the International Monetary Fund and the European Central Bank, are seeking and what the government in Athens was offering, the commission said. That gap amounted to up to €2 billion of “permanent fiscal measures on an annual basis,” the statement said.

Further discussion would take place on Thursday when so-called Eurogroup ministers hold their regular monthly meeting in Luxembourg.

But that, too, seems likely to result in deadlock unless both sides can come up with further concessions.

“Forging agreement is proving much more difficult than most expected,” Mujtaba Rahman, the practice head for Europe for the Eurasia Group, a political risk consultancy, said Sunday night.

“Unless Greek negotiators produce a credible set of reform proposals soon, this will amount to a spectacular miscalculation by Athens, resulting in default and capital controls in a matter of weeks,” he said.