The video, which was posted online on Thursday by Mekameleen, an opposition TV channel based in Turkey, appears to show two blindfolded men being shot in the head by uniformed soldiers.
In the video, one young blindfolded man is aggressively questioned by the officers who ask him if he is a member of the Abu Sanana family.
When he responds "No" and says he is from al-Awabadah, they ask him where his grandfather lives before forcing him to the ground and removing his blindfold.
One of the soldiers then shoots him in the head.
A person off-screen can be heard repeatedly shouting "Not just the head" as a second soldier then fires at the body on the ground.
Al Jazeera could not independently verify the video's authenticity. The Egyptian government has barred journalists from reporting on events in the Sinai Peninsula, where the army is battling a local affiliate of the Islamic State of Iraq and the Levant ( ISIL) group
Possible war crimesThe leaked video appears to depict part of a raid that the Egyptian army posted on social media on December 6.
That post included photos of three men in a field with guns next to them, who had been "killed in a raid" on an explosives storehouse.
Ahmed Mefreh, a lawyer and human-rights researcher, told Al Jazeera the killings amounted to war crimes.
"In the video, we see executions of unarmed people by forces wearing military uniform," he said.
"They are being shot in a direct way. International law considers this a war crime that clearly has to be investigated."
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