Mr. Tsipras’s government met in an emergency session on Saturday to discuss the implications. “The Greek government asks the I.M.F. for explanations whether pursuing the creation of bankruptcy conditions in Greece, just before the British referendum, is the fund’s official position,” Olga Gerovasili, a Greek government spokeswoman, said in a statement.

As a condition for it to stick with the bailout, the I.M.F. has pressed Germany hard to agree to Greek debt relief. The I.M.F. has leverage because the German Parliament might not agree to release funds to Greece unless the I.M.F. participates in the program. But Wolfgang Schäuble, Germany’s finance minister, has said he sees “no argument” for acceding to the I.M.F.’s demands.

The I.M.F. has countered that debt relief is needed not only to help the economy, but also because the Greek government is politically constrained in carrying out all the austerity needed to begin improving its tattered finances. Those frustrations boiled over in the private discussions published by WikiLeaks.

“These guys agree on something and then they give it up the next day,” Delia Velculescu, the I.M.F.’s mission chief for Greece, is reported to tell Mr. Thomsen in the transcript. “We have said this time and again, we know that they don’t do what we say,” she added. “It just doesn’t function. For them, everything is subject to change — if the authorities want it.”

Mr. Thomsen said he had expected that the refugee crisis in Greece might have pushed creditors to reach an agreement on debt relief quickly. In less than two months, Greece has become Europe’s de facto holding pen for more than 50,000 migrants since European countries shut their borders, preventing asylum seekers from reaching their preferred destination of Germany. Greece has been scrambling to manage a deteriorating situation, including riots in refugee camps and the beginning of a European Union program requiring the mass deportation of refugees from Greek islands starting on Monday.

“I am surprised that it has not happened, is that, because of the refugee situation, they take a decision, that they want to come to a conclusion,” Mr. Thomsen said of the creditors, according to the transcript.

If a conclusion does not come rapidly, he added, the I.M.F. would use the threat of quitting against the German chancellor, Angela Merkel, who cannot afford for Greece to spiral downward at a time when it is keeping the bulk of new refugees from reaching her country.

“You face a question,” Mr. Thomsen suggests the fund could tell Ms. Merkel. “You have to think about what is more costly: to go ahead without the I.M.F.,” he said, “or to pick the debt relief that we think that Greece needs in order to keep us on board.”