The civilians, mostly members of the Yazidi religious minority, eventually escaped via Syria with the help of Kurdish fighters from Iraq's neighbour to the west, but that route has now been cut.
"The mountain is besieged" again, and IS militants are "trying to climb the mountain on foot to fight the Yazidi volunteers," said Dawud Jundi, a commander of the forces defending the area, told AFP by telephone.
The IS push began Monday, when some 300 of the militants with armoured vehicles attacked and seized nearby villages and then turned their attention on the mountain itself.
On Mount Sinjar, "there are almost 2,000 families whose situations are very bad," he said.
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Mahma Khalil, a former Iraqi MP who is now another of the commanders in the area, said there were clashes on several sides of the mountain today.
The first siege of Mount Sinjar was a key moment in the conflict against the jihadist group, which spearheaded a offensive in June that has overrun large areas of Iraq.
The plight of the people trapped on the mountain helped prompt the United States to begin air strikes against the jihadists that have since been expanded into Syria and now involve a coalition of countries.