Gen. Joseph Votel, the commander of US forces in the Middle East, said that the refusal to follow orders occurred during the battle for the recently liberated town of Manbij, Syria.
ISIS leader Abu Bakr Al-Bagdadi told fighters in Manbij "to fight to the death" and "they didn't follow his direction," according to Votel, questioning how much command and control ISIS leadership has over its forces.
Still, he said that ISIS, also know as ISIL, has a "strong network" that relies on "guidance from centralized leadership."
Votel, speaking to reporters at the Pentagon, said he thinks that the Iraqi security forces "are on track" to recapture the key city of Mosul from ISIS by the end of 2016. But he warned that Mosul will be "a tough fight" now that the coalition is "into the heart of the caliphate."
He predicted ISIS would continue to use improvised explosive devices and human shields "that will make it more challenging for our people." But, he insisted, "We will prevail through that."
Votel also said ISIS would need to make some "tough decisions" about which parts of its territory to defend. He suggested the organization might cede sections of Mosul rather easily in order to focus on "revenue-generating" zones or "iconic" locations that are important to its status as a would-be state.
Turkey-Kurdish tensions in Syria
The general was also asked multiple times about the situation in Syria amid recent clashes between two critical American allies in the fight against ISIS, Turkey and the Syrian Democratic Forces, which includes Kurdish groups like the YPG.
Turkey has called the Kurdish fighters terrorists that Turkey sees as closely linked to Kurdish separatist groups based in Turkey. Ankara has repeatedly shelled Kurdish positions in northern Syria from within Turkey, but now Turkish-backed Syrian fighters and Turkish units within Syria have been involved in direct fights with SDF forces.
Votel lauded the contributions of both Turkey and the SDF, calling them both "critical" and adding that the recent clashes between them were "unhelpful."
"We don't want that. We're working to prevent that," Votel said, adding that the US military would only support efforts to combat ISIS and not pursue other goals in Syria.
"Our support to all parties is contingent upon the focus on ISIL," he said, noting that the Kurdish elements of the SDF had for the "most part" withdrawn east of the Euphrates River as per an earlier arrangement that sought to allay Turkish concerns by keeping Kurdish fighters in traditionally Kurdish regions of Syria.
Votel said that non-Kurdish units of the SDF, including Arab and Turkmen fighters, had taken over responsibility for securing Manbij.
Despite Turkish skepticism about the activity of Kurds in the SDF, Votel said that "they have lived up to their ... commitment to us," by pulling back.
In a statement, Tanju Bilgic, a spokesman for the Turkish Foreign Ministry, appeared to push back on US calls for restraint on Tuesday.
"We will continue the operation until terror does not bother Turkish citizens anymore," Bilgic said.
Meanwhile, US military officials have told CNN that Turkish and Kurdish forces have stopped fighting each other for the time being.
"We have received assurance that all parties involved are going to stop shooting at each other and focus on the ISIL threat," Col. John Thomas, a Central Command spokesman, told CNN.