The commander, Al-Sheikh Khayri, had returned from Germany, which has large Yazidi community, to defend his comunity, and was killed on Wednesday night, Khalaf Mamu told AFP.
"The humanitarian situation became very difficult because there is very little food," while fuel was also lacking, he said. Mamu put the number of fighters defending Mount Sinjar at about 1,200.
The ISIS group began a renewed push for the mountain on Monday after besieging it earlier in the year.
Some 300 of the terrorists with armoured vehicles attacked and seized nearby villages and then turned their sights on the mountain itself, commander Dawud Jundi said.
The first siege of Mount Sinjar, during which thousands of mainly-Yazidi civilians were trapped by IS, was a key moment in the conflict against the terrorist group, which spearheaded an offensive in June that has overrun large areas of Iraq.
Most of the people trapped in the first siege were eventually able to escape via Syria with the help of Kurdish fighters from Iraq's neighbour to the west, but that route has now been cut.
On Mount Sinjar, "there are almost 2,000 families whose situations are very bad," Dawud Jundi, a commander of the forces defending the area, told AFP."We don't have anything but light weapons," Jundi said.
According to the UN, dozens of Iraqi and Syrian religious minorities girls and women and children were abducted - possibly as many as 1,000, and were taken away to unknown destinations.
The Iraqi capital Baghdad has also seen a wave of bomb attacks against Shiite targets in recent days, with IS claiming responsibility for some.
At least 28 people were killed on Wednesday when car bombs went off near a maternity hospital and a service station in areas of the capital where Shiites have frequently been targeted.
A cleanup operation was underway in Baghdad's Karradah neighbourhood on Thursday morning after a car bomb exploded near a restaurant a day earlier.The blast killed 15 people and wounded 32, according to local police.
A separate explosion in Baghdad's eastern district of Sadr city killed 14 people and wounded 27, police added.
In the north of the country, Jabar Yawar Manda, spokesman and secretary general of Ministry of Peshmarga security force, said that the IS militants have occupied large swathes of territory in the northwest and still held big cities Mosul and Ramadi in their control.
Kurdish Peshmerga fighters were near Suleiman Beg Township before June 10, but now the area is occupied by IS militants, said Jabar Yawar. Jabar noted that weapons that Kurdish Peshmerga fighters used are not as advanced as those in the hands of the IS militants. “But the situation can be changed if the international community continues to offer military support to Kurdish forces”, he said.