The incident in the village of Iraq Burin was one of two fatal clashes in which four died, worsening tension between the sides and further complicating US-led efforts to restart stalled peace talks.
Palestinian doctors, who produced an X-ray image showing a bullet lodged in the brain of one of the dead, said Mohammed Kaddous, 16 and Osaid Kaddous, 17, were shot by live ammunition when soldiers opened fire at stone-throwing demonstrators.
The army says troops fired rubber bullets, following standard procedure for handling disturbances. Israel soldiers are only permitted to use live ammo in life-threatening situations.
A statement from the spokesman's office said the Israeli commander for the West Bank had named a brigadier general to head the investigation of what it called "the circumstances surrounding the deaths of two Palestinian protesters.” Palestinians said the protest held at the site was against land confiscations by a nearby Jewish settlement.
The Israeli spokesman said it could take some days before any findings were issued.
Separately, two Israeli soldiers faced court martial on Wednesday on a charge of endangering the life of a Palestinian boy by instructing him to open suspected booby-trap bag during the three week Gaza war that ended in January 2009. The bag turned out to be harmless.
The soldiers face a maximum three-year jail term if convicted.
