The statement was issued on Friday when at least 17 Palestinians lost their lives and more than 1,400 others sustained injuries when Israeli military forces opened fire on thousands of protesters who had flocked to a sit-in near the Gaza border.
On Saturday, the US objected to the adoption of the statement, which was proposed by Kuwait that represents Arab countries on the council, a Security Council diplomat told AFP.
The draft reaffirmed "the right to peaceful protest" and called for an "independent and transparent investigation" into the violence.
It also expressed "grave concern at the situation at the border" and shared the council's "sorrow at the loss of innocent Palestinian lives."
The statement also called "for respect for international human rights law and international humanitarian law, including protection of civilians," according to the draft seen by AFP.
Council members urged "all sides to exercise restraint and prevent a further escalation," said the draft.
On Saturday, Israeli Prime Minister Benjamin Netanyahu praised Israeli troops for killing the Palestinians and claimed their actions were aimed at guarding Israel.
Meanwhile, human rights organization Amnesty International has condemned the Tel Aviv regime’s policies of land confiscation and dispossession, calling on Israeli authorities to stop them.
The Britain-based organization, in a post published on its official Twitter page on Friday, stated Israel’s policies of land theft exacerbate the sufferings of the Palestinian nation, and deprive them of their basic rights.