The UN Secretary General, Antonio Guterres, has called for an independent investigation after 16 Palestinians were killed in clashes with Israeli soldiers on Friday.
The UN Security Council condemned the violence after an emergency session.
UN Deputy Political Affairs Chief Taye-brook Zerihoun told the council the situation in Gaza "might deteriorate in the coming days".
Palestinian President Mahmoud Abbas in a televised statement said that Israeli authorities bore full responsibility for Friday's deaths.
Abbas also sought international intervention that provides security for Palestinians.
Friday was the single deadliest day in the Israel-Palestine conflict since the 2014 Gaza War.
Clashes erupted when thousands of Palestinians marched to the border at the start of a six-week protest, dubbed the great march of return.
They were demanding that refugees be allowed to return to their homes in what is now Israel.
Six people killed and 400 were injured on the Gaza border.
Palestinians have pitched five camps near the border for the protest, from Beit Hanoun in the north to Rafah near the Egyptian border.