A Turkish government minister and spokesman, Bekir Bozdag, also accused Israel's most powerful ally, the United States, of helping fuel Palestinian outrage by moving the U.S. Embassy from Tel Aviv to Jerusalem.
Israeli Ambassador Danny Danon defended the use of force, calling the events at the border "violent riots".
Kuwait's Ambassador Mansour al-Otaibi and other ambassadors widely criticized the USA move at the meeting, saying it has the potential to ignite even more violence in an already unstable region.
On BBC Radio Four's Today programme, Israel's ambassador to the United Kingdom, Mark Regev said that following the USA decision, there are Latin American and European countries that will also be moving their embassies to Jerusalem.
Hamas, the terrorist organization that rules Gaza, is using the unveiling of the American embassy in Jerusalem as an "excuse" to encourage violence, the US State Department said Tuesday. The group had organized the action weeks ago to respond to the embassy move, but the protest took on a different tone as demonstrators learned of the mounting death toll in Gaza, which was "really horrific", an organizer said.
Belgian MEP Maria Arena says it's not the right time to call for that recognition.
That said, let's also note that numerous demonstrators were peaceful.
Israel considers the entire city its capital, while the Palestinians see east Jerusalem as the capital of their future state.
United Nations says Lebanon-Israel border 'quiet' after Syria flare-up
It also came just hours after President Donald Trump announced the withdrawal of the USA from the Iran nuclear deal. In strikes near the capital on Wednesday, the Observatory said at least 15 were killed, including eight Iranians.
"Israel will no longer hold back from defending its honor and will safeguard its borders and citizens", he wrote.
"They don't understand the difference, and Israel is losing points in the worldwide community because of what is happening in Gaza".
"Make no mistake, Hamas is pleased with the results from yesterday", she said.
Ngcukayitobi called on International Relations and Cooperation Minister Lindiwe Sisulu to cut all ties with Israel and expel the country's ambassador to South Africa, Lior Keinan.
On Facebook, he wrote: "I made a decision to return the embassy of Guatemala to the city of Jerusalem two days after the United States moved its embassy".
United Nations human rights spokesman Rupert Colville said Israel had a right to defend its borders according to worldwide law, but lethal force must only be used a last resort, and was not justified by Palestinians approaching the Gaza fence.
Its main ally the United States has backed that stance, with both saying that Hamas, the Islamist group that rules the coastal enclave, instigated the violence.
According to a statement released by the Palestinian Foreign Ministry on Tuesday, the head of the Palestine Liberation Organization's office in Washington, Husam Zomlot, would be leaving the U.S. on Wednesday.