Iraqi Kurdistan’s independence from Baghdad appears to be only a matter of time, presenting a tremendous challenge to Iraq’s future, according to the head of the US Defense Intelligence Agency.

“Kurdish independence is on a trajectory where it is probably not if, but when. And it will complicate the situation unless there’s an agreement in Baghdad,” Lieutenant General Vincent Stewart, head of the Defense Intelligence Agency (DIA), told a Senate hearing, according to Reuters.

Kurd militias are essential to the US-led coalition’s campaign to defeat Islamic State (IS, formerly ISIS/ISIL) in Iraq. The Kurds are also taking part in the battle of Mosul, where Iraqi forces are trying to force IS militants from their major stronghold.

Once Mosul is liberated and the Islamist ‘caliphate’ defeated, the widening rift between Iraq’s Shiite Arab majority and Kurds will still be there, Steward noted.

“Once ISIS is defeated in Mosul, the greatest challenge to the Iraqi government is to reconcile the differences between the Shia-dominated government, the Sunnis out west, and the Kurds to the north,” said the chief of military intelligence.

Iraqi Kurdistan has long sought to secede from Iraq, arguing that the Kurds have an inherent right to self-determination after suffering decades under the heavy-handed rule of Saddam Hussein and his predecessors. Led by long-time Kurdish leader and president of Iraqi Kurdistan, Masoud Barzani, the autonomous region’s political parties have worked out a roadmap for a future referendum on Kurdish independence.

Kurds, the leaders say, have their own ethnic identity, which does not fit in well in present war-torn Iraq. “We are not Arabs, we are our own Kurdish nation… At some point, there will be a referendum on the independence of Kurdistan, and then we will let the people decide,” Iraqi Kurdistan’s prime minister (and the president’s nephew), Nechervan Idris Barzani, told German Bild newspaper last October.

In the meantime, Iraqi Kurdistan’s president maintains that Iraq has no future as a viable entity. In early March, he predicted that Iraq faces the prospect of being split into two or more independent states, following the example of Czechoslovakia – a former socialist country that split into the Czech Republic and Slovakia in 1993.

On the other hand, the Iraqi government says the secession is not in Kurdistan’s best interests.

In neighboring Turkey, Kurdish communities are being subjected to a government crackdown sometimes involving armed force. Meanwhile, Syrian Kurds are now fighting Islamic State after seeing their people mass murdered in areas previously controlled by jihadists.

Iraqi Kurdistan has its own military, known as Peshmerga, which prevented Islamic State militants from capturing the oil-rich region of Kirkuk in 2014. The Kurds have long claimed sovereignty over Kirkuk, which is also inhabited by Turkomans and Arabs.

The autonomous region is determined to build up its military capabilities in a bid to become a sustainable independent state. On Monday, a Peshmerga official told Kurdistan24 news outlet that Kurdish leaders are considering the purchase of combat aircraft to establish a Kurdish airforce.

“Resolving the Kirkuk oil field and the revenues associated with the oil fields, resolving the ownership of the city of Kirkuk, will be significant political challenges for the Iraqi government,” General Stewart said, warning that Baghdad will face dire consequences if it fails to come to terms with the Kurds.

“Failure to address those challenges, coming up with a political solution, will ultimately result in conflict among all of the parties to resolve this and going back to what could devolve into a civil strife in Iraq,” the DIA head said.