The comments by Gen. Qassem Soleimani, the head of the Guard's elite Quds unit, come just after U.S. Defense Secretary Ash Carter accused Iraqi forces of lacking the "will to fight" in an interview aired the day before.
It wasn't clear whether Soleimani's remarks came as a direct response to Carter's, though tensions remain high between the two countries amid negotiations over Iran's contested nuclear program.
Soleimani said Iran and its allies are the only forces that can deal with Islamic State group, "Today, there is nobody in confrontation with (the Islamic State group) except the Islamic Republic of Iran, as well as nations who are next to Iran or supported by Iran," he said.
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Iran has offered advisers, including Soleimani, to direct Shiite militias fighting against the extremists. Iran has said it does not have combat troops fighting in Iraq, though some Revolutionary Guard members have been killed there.
Meanwhile in Syria, activist said government warplanes conducted more than 15 air raids on the historic central town of Palmyra and nearby areas, leaving some dead or wounded. The air raids on Palmyra came a day after the government said that Islamic State fighters have killed more than 400 state employees, troops and pro-government gunmen since they captured the town Wednesday.
The activists said the air raids were mostly inside the town and far from the famous archaeological sites that are among the Middle East's most spectacular.