"Islamic State brigades have now reached the border triangle between Iraq, Syria and Turkey. May God Almighty allow his mujahideen to liberate the whole region," it said in a statement.
The jihadist group listed the gains achieved over the weekend in what was its most significant territorial push since first sweeping across Iraq nearly two months ago.
It seized the large town of Sinjar yesterday, as well as two others in the same area. It took the town of Zumar the previous day and is now threatening Mosul dam, the country's largest.
"In a day-long series of battles involving a variety of weapons... The apostate enemies were humiliated, dozens were killed and wounded and hundreds fled."
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The Kurdish government has not provided casualty figures nor commented on reports that several Kurdish peshmerga fighters were captured.
The areas IS fighters took were regions the peshmerga moved into in the initial chaos that saw government soldiers retreat in the face of the jihadist offensive launched on June 9.
It also allows the Islamic State's men to move easily between Iraq's second city of Mosul, which they overran on June 10, and the Syrian border.