The ICC Chief Prosecutor hinted that her office would examine both Israeli use of force and Hamas use of human shields in Gaza for possible prosecution.
The UN office noted that Israeli security forces are required by worldwide 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.
Beleaguered by years of rocket attacks from next-door Gaza, residents of the frontline Israeli village of Nahal Oz seemed unmoved on Sunday by Palestinian mass demonstrations at the border and Israel's deadly response to them.
The number of protesters on Friday was larger than in recent days, but lower than it was last Friday.
"N$3 ot only did the President of the United States react by saying nothing, not only did the vast majority of members of Congress. been entirely silent about this frankly unconscionable use of force - the USA blocked a U.N. Security Council statement calling for an investigation of what happened", he said.
The Israeli military says its troops will only use live fire against people trying to sabotage the border fence, rolling burning tyres towards it or throwing stones.
But Israel says the militant group Hamas, which dominates Gaza, is staging the rallies in order to launch attacks.
In all, 22 Palestinians were killed in Gaza over the past week, among them 16 involved in last Friday's protests, according to Gaza health officials.
Koreas holds preparatory talks to set up Kim-Moon summit
North Koreans watch a report showing North Korea's Hwasong-12 intermediate-range ballistic missile launch in August 2017. North Korea may also be likely to sell on its technology to other states that may be more aggressive towards the UK.
In a statement on Saturday, the European Union called on Israel and the Palestinians to clarify the use of violence during clashes along the Gaza Strip border on Friday.
The demonstrators have revived a long-standing demand for the right of return of Palestinian refugees to towns and villages that their families fled from, or were driven out of, when the state of Israel was created.
Since 2005, 23 out of every 24 deaths caused by the conflict between Israelis and Palestinians have been Palestinian, Vox reported. Israel has come under mounting criticism for shooting dead unarmed Palestinian civilians protesting peacefully. Israeli forces used gunfire and tear gas to keep them away from the border fence.
"Concerning rules of engagement, soldiers treat any activity putting Israel's security in danger as terrorist acts", he said.
Israeli troops on the other side of the fence responded with live fire, tear gas, rubber-coated steel pellets and water cannons.
Hamza Abd al-Al, 20, and photojournalist Yasser Murtaja, 30, who were shot on Friday, succumbed to their wounds on Saturday.
The Palestine Red Crescent Society has "also warned of a shortage of medical supplies and of personal protective equipment for their 400-person team deployed across Gaza".