Barzani's remarks came after militants carried out a late-September attack on a security service headquarters in the Kurdish region's capital Arbil, killing seven people - a rare occurrence in an area usually spared the violence plaguing other parts of Iraq.
"We will not hesitate in directing strikes (against) the terrorist criminals in any place," Barzani said in an exclusive interview with AFP, when asked about the possibility of Kurdish action against militants in Iraq or Syria.
"Our duty is to protect the Kurds if we are able," he said.
But the long-time Kurdish leader made a distinction between that and being drawn into Syria's bloody civil war, which he said the Kurds must try to avoid.
"Our opinion is that the Kurds must stand at the same distance" from all parties in the conflict, so "the Kurdish people are not forced into a war" from which they will gain nothing, Barzani said.
But Syrian Kurdish forces have already been drawn into the fighting, clashing with jihadist groups fighting President Bashar al-Assad's troops who want to secure a land corridor connecting them to Iraq.
The violence has pushed tens of thousands of Syrian Kurds across the border, seeking refuge in Iraqi Kurdistan.
And Barzani has previously threatened to intervene in the Syrian conflict to protect Kurdish civilians, although officials have since backtracked on his remarks.
Barzani also said in the interview that Iraqi Kurdistan had provided military training to Syrian Kurds so they could defend their communities.
"A number of young (men) were trained, but truly not with the aim of entering the war," Barzani said.
In claiming the September 29 attack in Arbil, which killed seven security force personnel and wounded more than 60 people, al Qaeda front group the Islamic State of Iraq and the Levant also pointed to Syria.
The group said the attack on the Kurdish asayesh security service headquarters with suicide bombers, gunfire and car bombs was in response to Barzani's alleged willingness to provide support to the government in Baghdad and to Kurdish forces battling militants in Syria.
The attack was the first of its kind to hit Arbil since May 2007, when a truck bomb exploded near the same headquarters, killing 14 people and wounding more than 80.
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