Riyad Mansour, the Palestinian Ambassador to the UN, also called for investigations into the deaths of 18 Palestinians in clashes with the IDF as part of the "March of Return" protests in the Gaza Strip.
"The Palestinians that were killed or injured were exercising their right to peaceful protest," the letter states. "However the occupying Power had once again, in a premeditated manner, adopted a shoot-to-kill policy."
The IDF has stated at that at least 10 of those killed were known terrorists.
The letter quoted a recent column by left-wing Israeli journalist Gideon Levy and a press statement by B'tselem — The Israeli Information Center for Human Rights in the Occupied Territories, describing the scene as a "massacre."
Since protests began on the Gaza border on Friday, over 1,500 Palestinians have been wounded according to the Gaza health ministry.
Israeli officials, including Defense Minister Avigdor Liberman, have stated numerous times that Israel would not let its sovereignty be breached or allow harm to come to its border fence with Gaza.
"I warn (Gaza protesters) against continuing the provocation. We have set clear game rules and we do not intend to change them. Every person who comes close to the fence is endangering their lives," he said on a visit to the border.
"This was a well-organized provocation by Hamas's armed wing in an attempt to harm our sovereignty, to disrupt daily life and to disturb Israelis on their Seder (traditional Passover meal) night. We are doing what we must do."
In Gaza, protesters have begun gathering thousands of mirrors which they hope to use to blind Israeli soldiers on the other side of the fence in planned protests this Friday. The protesters say they also intend to use laser pointers to distract Israeli army sharpshooters.
Reuters contributed to this report