As the council met Tuesday, U.S. Ambassador Nikki Haley laid blame for Monday's violence on the Hamas extremists who rule Gaza and insisted it had nothing to do with the opening of a U.S. embassy in contested Jerusalem, a move that infuriated Palestinians.
Israel regards all of Jerusalem, including the eastern sector captured in the 1967 Middle East, as its capital.
Guatemalan President Jimmy Morales dedicated the embassy just two days after a high-powered American delegation marked the transfer of the U.S. Embassy.
Prime Minister Benjamin Netanyahu said it was fitting since Guatemala also followed the U.S.to be the second country to recognize Israel 70 years ago.
The US and Guatemalan moves break with decades of global consensus.
Palestinians have also held demonstrations on the Gaza border for their right of return to their homes, now in Israel.
Israel was criticised internationally for killing unarmed Palestinians.
Protesters set tires ablaze, sending thick plumes of black smoke into the air, and hurled firebombs and stones toward Israeli soldiers across the border.
Pushing back against foreign censure of its army's actions, Israel has - with Washington's backing - accused Hamas of using civilians as cover for attacks across the frontier fence and to distract from Gaza's internal problems.More news: Thomas Tuchel named as new PSG manager
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"We are analyzing what kind of legal steps can be taken", he said, according to Turkey's Hurriyet daily, adding that his country was giving legal aid to the Palestinians.
The admission came one day after Björn Stritzel, a reporter for the German tabloid BILD, tweeted so-called "martyrdom pictures" of Hamas militants killed in the violence.
Early on Thursday, Israeli aircraft hit four Hamas targets in the northern Gaza Strip in response to heavy machine gun fire that struck houses in the Israeli town of Sderot, the Israeli military said.
On Wednesday, Israeli officials seized upon remarks by a senior Hamas member who said 50 of the 62 Palestinians killed this week were members of the group, arguing it showed the protests were not peaceful.
On Tuesday, Israel's military allowed eight trucks full of humanitarian aid and medical supplies to enter the Gaza Strip. Hamas says the demonstrations are a popular outpouring of anger, and Israel carried out a "massacre" in response. "But that's when you have leaders who've decided that they abandon the goal of war and destruction and annihilating the other side", Netanyahu said.
Patientswith gunshot wounds filled wards and hallways in Gaza's under-equipped and overwhelmed hospitals, with dozens still waiting in line for surgery a day after the deadliest day of violence since the 2014 Gaza war.
The Jew-hating United Nations had some harsh words.for Israel.
Hamas denied it had come under Egyptian pressure to curb the protests, which provoked global condemnation of Israel's deadly tactics in putting down the unrest.
Turkey expelled Israel's ambassador and consul general and several European countries summoned the Israeli ambassadors to their foreign ministries for questioning and called for an global investigation.