The breakthrough coincided with recent attacks by Iraqi forces against hideouts of the ISIL terrorists in the Sinjar area of northwestern Iraq on 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 Syria 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 told AFP.
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 told AFP. "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 air drops to those still stranded.
Thousands of terrified people, mostly from minorities that have been persecuted by the ISIL terrorists, ran to the mountain a week ago when the armed insurgents 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, warning that many more would perish if decisive action was not taken in the following 48 hours.
A spokesman for the UN Office for the Coordination of Humanitarian Affairs in Iraq said officials had been reporting to the UN that 15,000 to 20,000 people had escaped the siege.
NTJ/MB