Nine Palestinians were killed on Friday as Israel ignored calls for restraint in its use of force against unarmed protesters in Gaza for the second week in a row.
The UN office noted that Israeli security forces are required by global human rights law to respect the rights to peaceful assembly and expression and to use, to the extent possible, non-violent means to discharge their duties.
Israeli troops opened fire on three Palestinians who were spotted crossing into Israeli territory from the northern Gaza Strip on Sunday afternoon, the army said, amid heightened tensions along the Gaza border. UK Opposition Leader, Jeremy Corbyn condemned the killings by Israeli soldiers in a statement Saturday.
Gazans, including Palestinian refugees and their descendants seeking to regain ancestral homes in what is now Israel, have set up tent encampments a few hundred meters inside the 65-kilometer (40-mile) fence that separates Israel from the Gaza Strip.
"The circumstances of the breach are being investigated", the army said. It says its snipers carefully targeted only the main "instigators", and accuses Hamas of using the crowds as cover to stage attacks.
As last Friday's protest got under way, six Israeli high school students who were on a study visit to Nahal Oz, clambered up an abandoned guard tower to peer into Gaza.
Palestinians in the Gaza Strip have ferried carts of tires to the border fence with Israel in recent days.
Thousands of protesters - Israel estimated 20,000 - gathered in locations near the border east of Khan Yunis, in the south of the blockaded Palestinian enclave, and east of Gaza City, among other spots.
Israel has defended the wars as a response to intense rocket hearth from Hamas-ruled Gaza, and notes the group's historical past of suicide bombings and different lethal assaults, particularly through the second Palestinian rebellion early final decade.
He said U.N. Mideast envoy Nickolay Mladenov had been in touch with Israeli and Palestinian officials to reinforce "the need to allow people to demonstrate peacefully".
The following day, Israel's military said in a tweet that "Nothing was carried out uncontrolled; everything was accurate and measured, and we know where every bullet landed".
The Palestinian Red Crescent Society, which has established five advanced medical posts near various protest sites, also warned of a shortage of medical supplies and of personal protective equipment for their 400-person team. Hundreds more suffered other injuries, including tear gas inhalation, the officials said.
On Saturday, the European Union raised questions over whether Israeli troops engaged in "proportionate use of force".
"If they are actively attacking the fence, if they are throwing a molotov cocktail that is within striking distance of Israeli troops or similar activities, then those persons, those rioters, become, may become, a target", said Lt. Col. Jonathan Conricus. Hosam Salem, a photographer at the scene of the incident told Al Jazeera on Friday that he witnessed Murtaja drop to the ground after he was shot by Israeli forces. Israel has deployed more than 100 snipers with orders to shoot anyone approaching the buffer zone near the Gaza border.