Israeli soldiers aim towards Palestinian youths during clashes in the West Bank town of Hebron on Oct. 4, 2015. (AFP/Hazem Bader, File)
Palestinian protesters said they found the footage on a camera that was dropped by an Israeli soldier during clashes near Ramallah.
Palestinian activists later published the footage on Facebook, saying that it "refuted" the Israeli army's claim that Israeli forces only opened fire on Palestinians posing an imminent threat.
The footage includes several snippets of conversation between two people said to be Israeli soldiers, one a sniper and the other his commanding officer, as they discuss opening fire on Palestinian protesters.
In one early scene, the officer congratulates the sniper for shooting a Palestinian "in his butt." In other scenes, he repeatedly says: "Wow, very cool," after the sniper shoot and hits protesters.
"Come on, you are allowed to shoot," the officer urges the sniper, after which the sniper fires a shot and says: "I got him! I got him!"
In a later scene, the officer asks: "Did you hit him?" to which the sniper replies: "Of course I did, bro."
A final scene shows the men climbing into an Israeli military jeep, appearing to show the interior of the vehicle.
The authenticity of the video footage could not initially be confirmed. An Israeli army spokesperson said she was looking into the reports.
Both local and international rights groups have repeatedly criticized the Israeli army for its excessive use of force and for killing and wounding Palestinians who did not pose an imminent threat.
Thousands of Palestinian protesters have been wounded by Israeli forces since a wave of unrest swept the occupied Palestinian territory in October.