The same day, Israeli troops shot dead several dozen Palestinian protesters on the Gaza border.
Israeli snipers fired live ammunition at protesters and used tear gas dispersed from drones.
Two UN diplomats said members could not reach unanimous agreement on a proposed statement, circulated by Kuwait, that would have expressed "outrage and sorrow" over the killings and sought an independent investigation.
It also reaffirmed United Nations resolutions on the status of Jerusalem, saying that recent events had "no legal effect" under worldwide law.
The UN Security Council planned to meet Tuesday to discuss the violence, though it was not clear what might come out of the session.
The Gaza Health Ministry said eight minors were among those killed by Israeli fire, and that a 9-month-old infant, Layla Ghandour, had died of tear gas exposure. CNN journalists there heard gunfire in spurts and saw a tank moving towards the fence in the border area of Malaka.
The march in Cape Town echoed the Palestinian protest - called the "Great March of Return" - which started in March this year and has seen daily protests along Israel's border fence with Palestinian territory.
Violent protests also could take place in Jerusalem and the West Bank, the IDF warned.
"Many of them, shot in the back".
Turkish Prime Minister Binali Yildirim also said that Muslim countries should review their ties with Israel after Monday's violence. "We believe that, because of our history, South Africa has the legitimacy and authority to act as steward in brokering peace in the Middle East".
The legislation, which became law in 1995, contained a clause that allowed presidents to postpone its enactment to protect national security.
Although Trump has said his declaration does not set the final borders of the city, his recognition of Jerusalem as Israel's capital has been perceived by both Israel and the Palestinians as taking Israel's side in the most sensitive issue in their conflict. The city is also home to deeply holy sites for Jews and Christians.
Indications suggest that some of the demonstrators in Gaza were protesting the new U.S. Embassy in Jerusalem. He says President Donald Trump's strategy is key.
When asked about possible peace talks between Israelis and Palestinians - and the timing of the most recent White House contact with Palestinian leaders - Shah said, "Well, I don't honestly have an answer for you on that".
Israeli President Benjamin Netanyahu expressed his gratitude towards United States President Donald Trump for opening the USA embassy in Jerusalem.
In a statement, the Foreign Ministry said the perpetrators of Israel's brutal action which led to the deaths of more than 50 Palestinians who were protesting against the opening of the United States embassy in Jerusalem on May 14 must be held accountable for the crime against humanity.
Tuesday was to have been the climax of six weeks of protests in Gaza meant to dramatize their refugee status on the day Palestinians mark the "nakba", or "catastrophe", of their displacement by Israel's 1948 creation.