Nechirvan Barzani told the BBC that his “top priority” was to protect KRG-administered areas in the north-east.
He also called for Iraq’s Sunni Arabs to be given their own autonomous zone.
In the past week, Peshmerga fighters have taken control of several cities and towns deserted by Iraqi soldiers in the face of the jihadist advance.
They include the city of Kirkuk, which along with the surrounding oil-rich province of Tamim, is at the heart of a political and economic dispute between the KRG and the Arab-led central government in Baghdad.
Speaking to the BBC’s Jim Muir in Irbil, Mr Barzani was emphatic that the Kurds’ top priority now was to defend their own areas.
He ruled out using Peshmerga fighters – thought to number around 75,000 – to drive out the Islamic State in Iraq and the Levant (ISIS) from Sunni Arab areas, saying it was not just a question of terrorism.
The KRG’s prime minister blamed the crisis on policies pursued by the Shia Prime Minister in Baghdad, Nouri Maliki, whom Sunni Arabs have accused of discriminating against them and monopolising power.
“It’s not only ISIS. It’s the result of the wrong policy in Baghdad vis-a-vis Sunni areas. It’s about the Sunni community feeling neglected,” he said.
Mr Barzani, the nephew of Kurdistan’s President Massoud Barzani, believed Iraq would never be the same.
“I don’t think it can stay together. As I said: Iraq before Mosul, and Iraq after Mosul. So now we have to sit down and find a formula how to live together, but if we think that Iraq will go back like before Mosul, I don’t think so – it’s almost impossible.”
Creating an autonomous Sunni Arab region might be the answer, he said.
“We have to leave it to Sunni areas to decide, but I think this is the best model for them as well. First, they have to take a decision: what they want exactly. And in our view… the best way is to have a Sunni region, like we have in Kurdistan.”
“There is no trust between Maliki and the Kurds, and even with Shia groups. So, in my view, [a political solution] is difficult,” he added.
Mr Barzani said the US should help Iraq, but only on the condition that Mr Maliki – whose State of Law bloc won the most seats in April’s parliamentary elections – was denied a third term in office.
“If the situation can go back to normal without Maliki, I think they have to do it.”
Iran is reported to be pressing the Kurds to join the campaign against ISIS and its allies. But, our correspondent says, they clearly would not even consider it, without a major change in Baghdad.