Forces led by the Kurdish Peshmerga and backed by US airstrikes on Thursday launched the attack to retake the strategic town of Sinjar, near the Syrian border, from Islamic State.
Hours later, the Security Council of Iraq’s autonomous region of Kurdistan said they had seized a stretch of the highway.
The main supply route runs from Islamic State’s stronghold in the northern Iraqi city of Mosul to the city of al-Raqqa, the jihadist group’s de-facto capital in Syria.
“Sinjar is now isolated from Tal Afar and Syria,” the Kurdistan Security Council said, referring to an Islamic State-controlled town north of Mosul.
Peshmerga commanders said their forces were advancing towards the centre of Sinjar, about 120 kilometres north-west of Mosul.
Islamic State claimed that its insurgents had repulsed an attempt by the Peshmerga to storm the village of Kolat on the outskirts of Sinjar.
Dozens of Kurdish soldiers were killed and wounded in the ensuing fighting, the radical group claimed in a tweet circulated by its supporters.
The claims could not be independently verified.
The offensive, called Operation Free Sinjar, is also aimed at setting up a buffer zone to protect Sinjar and its inhabitants from artillery shelling by Islamic State.
An estimated 7,500 Peshmerga personnel are engaged in the ground attack, according to the Kurdistan Security Council.
Fighters from the Kurdistan Workers Party (PKK) and affiliated militias of ethnic minority groups are also taking part in the battle for Sinjar, the Firat News Agency, close to PKK, reported.
The battle-hardened Peshmerga have been instrumental in the US-backed military campaign to dislodge Islamic State from the areas it seized in a blitz in northern Iraq more than a year ago.
Islamic State overran Sinjar last year, forcing thousands of the Yezidi minority there to flee the mountain town.
The move prompted the United States to start an air campaign against the extremist group in Iraq.
Sinjar is one of several areas where administrative control is disputed between Kurdistan and Iraq’s central government in Baghdad.