"Thanks to (the Kurds') opposition and the help of their friends in the coalition, the spine of the Islamic State is broken," Barzani said after talks with Hungarian Prime Minister Viktor Orban in Budapest.
Hungary recently joined the fight against IS by committing to send some 150 soldiers to Iraqi Kurdistan's capital, Arbil.
Barzani said that although "the danger is not over", he was hopeful the days of the brutal militant organisation were numbered.
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The Kurdish president is in Budapest on an official state visit after wrapping up a trip to Washington where he met US President Barack Obama to discuss the situation in Iraq.
Barzani appealed for more humanitarian aid and asked the US to arm his Peshmerga forces directly instead of passing though the federal government in Baghdad.
The Peshmerga, backed by US air strikes, have prevented IS from advancing far from the mainly Arab cities they have seized in Iraq and into the area controlled by the Kurds.
But Barzani warned that his region was now dealing with more than one-and-a-half million refugees and internally displaced people" who have fled IS.