“Look at the Turks, they are standing by,” he said. “And the Americans are bombing.”

The battle began in September as fighters with the Islamic State, also known as ISIS or ISIL, stormed through dozens of villages and appeared, in short order, on the verge of taking Kobani. Initially, United States officials said the town was of little strategic value and that the militants were likely to win.

But as the United States and its allies began bombing, and Islamic State fighters kept rushing reinforcements to the front, it suddenly became the main battlefield of the broader conflict. Turkey ultimately allowed Iraqi Kurdish fighters to transit its territory, and the Americans dropped weapons and ammunition to the Kurds, stalling the advance of the Islamic State fighters. Today, the fight has become a grinding war of attrition, a grueling house-by-house battle.

Gen. Lloyd J. Austin III, head of the United States Central Command, said last month that the Islamic State had made a decision that Kobani would be its main effort. Referring to the Islamic State, he said, “as long as he pours, you know, legions of forces there into that area, we’ll stay focused on taking him out.”

In a recent video, the Islamic State called Kobani “a haven for every enemy of the caliphate.” In the propaganda war that Kobani has become, the militant group tested a new form: It used a British hostage, John Cantlie, in the role of news correspondent, broadcasting a report from the top of a building in Kobani claiming — falsely — that it controlled 90 percent of the city and was on the verge of victory.

The battle is complicated by Turkey’s role, which sees some of the Kurdish factions as terrorists determined ultimately to destabilize Turkey to create a Kurdish state. Turkey, some analysts said, has been content to sit back and see two of its enemies — Kurdish separatists and Islamist militants — killing each other.

Turkey has insisted that a group of non-Islamist rebels, with the Free Syrian Army, or F.S.A., also join the fight for Kobani. These rebel fighters have gone reluctantly, because they see their primary enemy as the Assad government.