The Kurds have kept pumping oil anyway, betting that their American allies, who have pressured them to abide by the Iraqi oil law, will soften their stance, and that buyers will come forward. But as oil prices have plummeted, and as Iraq and the United States have refused to budge, the odds are getting longer by the day.

For now, Kurdish officials are sticking to a long-term view of the confrontation, despite its high cost at a time when the government is all but broke. They believe that, eventually, the oil glut this fall will end, and that international buyers will need Kurdish crude and support their nationalist aspirations.

“The ships going out to the international seas are testing the waters,” said Khalid Salih, a former senior adviser to the Kurdish Ministry of Natural Resources. “Suddenly, you will see and hear breakthroughs.”

American officials who want Kurdistan to remain a part of Iraq, and want the Kurdish pesh merga to keep fighting Islamic State militants where the Iraqi Army cannot, are pressing the two sides to work things out. Negotiations are underway, but officials with knowledge of the talks say in private that little progress has been made.

Kurdish politicians have given the new Iraqi prime minister, Haider al-Abadi, roughly another month to settle, restoring payments and giving them more freedom to market oil, or they will not participate in the Iraqi government. Mr. Abadi has said he is willing to compromise, but so must the Kurds.