"I strongly condemn yesterday's apparent extra-judicial execution of a Palestinian assailant in Hebron in the occupied West Bank," UN Special Coordinator for the Middle East peace process Nickolay Mladenov said in a statement.
"This was a gruesome, immoral and unjust act that can only fuel more violence and escalate an already volatile situation."
He welcomed, however, Israeli Defence Minister Moshe Yaalon's condemnation of the incident and called on the Israeli authorities to "swiftly bring to justice" the alleged perpetrator.
The clip, which was widely shared online and shown by state-owned and commercial Israeli TV channels, shows what appears to be one of the most flagrant cases of Israeli forces' alleged use of excessive force so far in the wave of Israeli-Palestinian violence that erupted in October.
The incident was immediately condemned as an "execution" by Israeli rights group B'Tselem and as a "war crime" by Palestinians.
The incident also fired up Israeli politicians and added heat to the debate over Israeli forces' response to the current wave of violence which has left 200 Palestinians and 28 Israelis dead.
Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, according to Israeli authorities.
But the Israelis have also been accused of using excessive force in some cases, charges which they have firmly denied.
"The attacks on a soldier who protects all of us before the investigation has even started harms the military, harms Israel's standing in the world, and is harmful towards our attempts to thwart future attacks," he said in a statement.
Former foreign minister Avigdor Lieberman also defended the shooting, saying it was "hypocritical and unfair to gang up against the soldier."
"Better a soldier who makes a mistake but stays alive than a soldier who gets killed by a terrorist because he hesitated," he said.