The peshmerga closed in on Sinjar town south of the mountain and Tal Afar to its east. If successful, the move would significantly alter the map of the Islamic State (IS) group's self-declared cross-border "caliphate" and isolate its Mosul hub.
The autonomous Iraqi Kurdish region's peshmerga troops reached the flanks of Mount Sinjar with food and other aid three days after launching a vast operation in the region backed by US-led coalition air strikes.
As the convoy worked its way up the mountain, a 60-kilometre-long (40-mile) ridge where civilians and fighters had been trapped since September, people swarmed vehicles to get food.
"I haven't seen an orange since September," said a 10-year-old girl as the peshmerga distributed fruit and other food.
The civilians, some of whom had sought refuge on Sinjar after being displaced from nearby villages by IS fighters, looked exhausted, their skin sunburnt and clothes caked in dirt.
"We had barely received any aid in 75 days. It stopped coming when the Islamic State cut the road," said Hassan Khalaf, a gaunt 45-year-old.
"What we need now is aid. We want them to save us," he told an AFP journalist travelling with the peshmerga convoy.
Tens of thousands of members of the Yazidi religious minority were trapped on the mountain for days in the searing August heat in a first siege that sparked fears of genocide and was one of the reasons that led US President Barack Obama to launch an air war against IS.
Many were eventually evacuated when a coalition of Kurdish forces opened a corridor to Syria, and on Saturday the same factions were trying to reopen that route.
A statement from the Kurdish president's son, who also heads the Kurdish Regional Security Council (KRSC), said the peshmerga had cleared villages on the northern side of the mountain.
The Syrian Kurdish YPG group, which has been leading the battle against the jihadists in the town of Kobane on the Syrian-Turkish border, was moving south to join up with the peshmerga.
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It said it recaptured several villages from IS on the Iraqi border, which was confirmed by the Syrian Observatory for Human Rights monitoring group.
Securing that corridor will make it possible to evacuate some of the civilians on Sinjar to Iraqi Kurdistan via Syria.
The peshmerga are also receiving crucial support from Yazidi tribal fighters.
On Wednesday, the peshmerga launched what they have described as the largest operation yet against the IS since it overran major parts of Iraq in June.
One of the heaviest series of coalition air strikes paved the way for 8,000 peshmerga to advance.
They soon retook several villages and forced many IS fighters to flee west to Syria or east to Mosul, Iraq's second city and the de facto IS capital in the country.
The KRSC said peshmerga forces had used their momentum to move in on Sinjar town on the mountain's southern side.
The peshmerga "succeeded in taking complete control of it and nearby villages," it said on Twitter, although sources on the ground said it was not yet clear that the jihadists had been ousted from the town.
Qassem Shasho, a Yazidi Kurdish commander, said peshmerga forces had reached Sinjar town but have not yet entered as it has to be cleared of militant booby-traps.
On Friday, residents reported that peshmerga forces were closing in on Tal Afar, pounding IS positions and forcing civilians and fighters to flee.
Tal Afar is a large town between Sinjar and Mosul. Large numbers of Shiites and Turkmens had to flee the town in June.
The area between Mosul and the Syria border is considered the heart of IS territory in Iraq. If peshmerga can hold newly retaken ground or make further gains, remaining jihadist positions in and around Mosul will find themselves more isolated.
Some Iraqi political and military leaders have been pushing for swift action to retake Mosul, but US military experts and others have warned that neither the peshmerga nor the federal forces would be ready for some time.
Nevertheless, jihadists in Mosul appear to be digging in, building berms and trenches around the city, cutting the phone network and preventing civilians from leaving.