"The Islamic Republic of Iran was the first state to help us...And it provided us with weapons and equipment," Barzani said at a joint news conference with Iranian Foreign Minister Mohammad Javad Zarif.
Militants led by the Islamic State (IS) jihadist group launched a major offensive in June that overran large areas of Iraq, and began a renewed push earlier this month that saw Kurdish forces pushed back towards their regional capital of Arbil.
The Kurdish setbacks sparked a campaign of US air strikes in northern Iraq and an international effort to provide them with arms and ammunition, and they have since managed to claw back some territory from the militants.
There have been reports of Iranian forces fighting in Iraq, and despite Zarif's denial, evidence points to a more direct military role by Tehran.
State media reported that an Iranian pilot was killed fighting in Iraq, and several Iranian Su-25 warplanes are also in the country.