The breakthrough coincided with US air raids on Islamic State fighters in the Sinjar area of northwestern Iraq Saturday.
Shawkat Barbahari, an official from the autonomous Kurdish region of northern Iraq put the number of people who escaped the siege and crossed back into Iraqi Kurdistan at 30,000.
“The Kurdish peshmerga forces have succeeded in making 30,000 Yazidis who fled Mount Sinjar, most of them women and children, cross into Syrai and return to Kurdistan,” said Barbahari, who is in charge of the Fishkhabur crossing with Syria.
“Most of them crossed yesterday and today, this operation is ongoing and we really don’t know how many are still up there on the mountain, he said”
Lawmaker Vian Dakhil, who is from the Yazidi minority most of the Mount Sinjar displaced belong to, said 20,000 to 30,000 had managed to flee and were now in Iraqi Kurdistan.
“20,000 to 30,000 have managed to flee Mount Sinjar but there are still thousands on the mountain,” she said “They have arrived in Kurdistan.”
“The passage isn’t 100 percent safe. There is still a risk,” she added, as the international community ramped up efforts to provide food and water by airdrops to those still stranded.
Thousands of terrified people, mostly from minorities that have been persecuted by the jihadists, ran to the mountain a week ago when militants overran the Sinjar region.
They found themselves trapped on the mountain in the searing summer heat with little to eat or drink.
Dakhil and others have said that many children and elderly people have already died and warned on Saturday that many more would perish if decisive action was not taken in the following 48 hours.
A spokesman for the U.N. Office for the Coordination of Humanitarian Affairs in Iraq said officials had been reporting to the U.N. that 15,000 to 20,000 people had escaped the siege.
He stressed that the U.N. was not directly involved in the exfiltration and could not confirm those numbers but stood ready to assist those crossing back into Kurdistan’s western Dohuk province, where the U.N. has a presence.
Kurdish forces from Iraq, Syria and Turkey have worked together in a bid to break the siege of Mount Sinjar and rescue the displaced.