After talks with President Barack Obama in Washington, Massud Barzani thanked US-led forces for their air support in the battle against the jihadists, but called for more humanitarian aid.
"We are proud of what we have achieved, because we believe we are on the frontline fighting on behalf of the free world this brutal terrorist organization," Barzani said.
"And it was by the hands of the peshmerga forces that they were able to destroy the myth of ISIS being this invincible force, but this has been a costly war."
Barzani said 1,200 Kurdish peshmerga troops have been killed fighting to hold back the IS forces that swept out of their bases in Iraq and Syria last year and seized several cities.
Kurdish forces prevented IS from advancing far from the mainly Arab cities they have seized in Iraq and into the area controlled by Barzani's autonomous Kurdish region.
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But they now find themselves dealing with "more than one-and-a-half million refugees and internally displaced people," many from ethnic and religious minority groups that are prey to the Sunni Islamist extremists.
"We believe that we have a humanitarian as well as a national responsibility," he told guests at Washington think tank the Atlantic Council. "But of course the burden is huge and we cannot afford it alone.
"That's why we call upon the United States and our friends in the international community to come and help the Kurdistan regional authority with these needs."
Barzani said he had met with the leaders of the Christian, Turkmen and Yazidi minorities and had assured them that the Islamic State threat can be defeated.
And he told them: "We do not want any of you to think about leaving the country, going to be asylum-seekers abroad. I assure you that we will be together. Either we will live freely in our country or we will die together."
The Kurdish leader confirmed he regarded his Tuesday meeting with Obama as successful, and that he believes the United States will find a way to better arm his forces, but would not be drawn on specific pledges from the US side.