The meeting began with a moment of silence for dozens of Palestinians killed by Israeli forces on Monday, the bloodiest day there since a 2014 Israeli war on the Palestinian enclave.
Joanna Wronecka, Poland's ambassador, called for the gesture of remembrance in her role as current council president.
Kuwait had called for the session after Monday's killings.
From US friends to foes, most ambassadors announced their opposition to the US embassy move. But the main focus of the debate was the violence at the Gaza border.
Almost all ambassadors said Israel bears a responsibility to keep its response proportionate, and not use live ammunition on civilians.
Olof Skoog, Sweden’s representative said that lethal force should be exercised with restraint, Press TV reported.
Francois Delattre, the French ambassador, said the violence threatens to engulf the Mideast region. “The situation in the Middle East is close to a perfect storm,”
Karen Pierce, the British ambassador, voiced support for a probe into Monday’s killing, then stated London’s position to the US embassy opening in Jerusalem al-Quds.
“Our position on the status of Jerusalem and moving the American embassy is well known,” she said. “The status of Jerusalem [al-Quds] should be determined in a negotiated settlement between Israel and Palestinians, and Jerusalem should ultimately be the shared capital of the Israeli and Palestinian states.”
Sasha Llorenty, Bolivia’s envoy said, “The unilateral decision by the United States to move its embassy to Jerusalem does nothing but inflame spirits.”
“The United States, which supports the occupying power, has become an obstacle to peace. It has become part of the problem, not part of the solution.”
The envoys from China, Sweden and the Netherlands also went out of their way to reiterate their government’s position that Jerusalem [al-Quds]’s status should be left to negotiations, and their intention to keep their embassies in Tel Aviv.
Speaking at the beginning of the session, Nikki Haley, the US ambassador to the United Nations, defended the Israeli use of force against peaceful Palestinian protesters, saying that the Tel Aviv regime had reacted with restraint in its military response to protesters at the Gaza border. She also dismissed suggestions that the violence was caused by the opening of the US embassy in Jerusalem al-Quds.
"No country in this chamber would act with more restraint than Israel has," Haley told the Council. "In fact the records of several countries here today suggest they would be much less restrained," she said.
The United States has already blocked the adoption of a UN Security Council statement that called for an “independent and transparent investigation” into Israel’s killing of Palestinian protesters on the Gaza border.
The statement, drafted by Kuwait ahead of a meeting on Tuesday, expressed “outrage and sorrow" at the deaths of at least 58 people during demonstrations over the opening of the American embassy in Jerusalem al-Quds.
It also demanded that all countries comply with a decades-old Security Council resolution calling on them not to station diplomatic missions in the occupied holy city.
The UN Middle East peace envoy Nikolay Mladenov said Tuesday there was "no justification" for the violence in Gaza as he briefed the 15-member council.
Mladenov called Monday a "day of tragedy" and urged the international community to put their efforts toward "preventing an explosion that can drag the whole region into deadly confrontation."
Several Muslims and Western countries have denounced the violence against Palestinians.
Belgium on Tuesday demanded a UN inquiry into the violence in Gaza and summoned Israel's ambassador to the foreign ministry after she described all the Palestinian victims as "terrorists."
Belgium's Foreign Ministry said it summoned ambassador Simona Frankel over her remarks while Prime Minister Charles Michel said, "We call for an international inquiry led by the United Nations."
Germany says it supports calls for an independent investigation into the killing of dozens of Palestinians by Israeli forces during protests in Gaza.
Government spokesman Steffen Seibert told reporters in Berlin on Tuesday that the violence "concerns us greatly and it's terrible that so many people lost their lives, including minors."
Turkey has asked Israel's ambassador to temporarily leave Turkey.
Anadolu, Turkey’s official news agency news agency said Tuesday that the Turkish foreign ministry notified Eitan Na'eh, the Israeli ambassador that "it would be appropriate for him to return to his country for some time."
The ministry summoned the ambassador to protest Israel's use of deadly force on Palestinians and the US decision to relocate its embassy there to Jerusalem al-Quds.
Turkey has also called home its ambassadors to Washington and Tel Aviv for consultations.
Israeli gunfire killed 59 Palestinians and wounded over 2,700 in the Monday clashes, the highest toll in a single day since a series of protests demanding the right to return to ancestral homes began on March 30.
The embassy inauguration also coincides with the climax of a six-week demonstration on the 70th anniversary of Nakba Day (Day of Catastrophe), May 15, when Israel was created.
The occupied territories have witnessed new tensions ever since US President Donald Trump on December 6, 2017 announced US recognition of Jerusalem al-Quds as Israel’s “capital” and said Washington would move US embassy to the city.
The dramatic decision triggered demonstrations in the occupied Palestinian territories as well as Iran, Turkey, Egypt, Jordan, Tunisia, Algeria, Iraq, Morocco and other Muslim countries.