A 51-year-old man was also killed in Tuesday's more muted demonstrations, along with another protester, bringing the total number of dead to 60.
The US joined Israel in blaming Hamas for the deaths, with the Israeli military suggesting the terrorist group attempted armed violence under cover of the demonstrations against Donald Trump’s move of the US embassy to Jerusalem.
Turkey and South Africa, staunchly aligned with the Palestinians, recalled their ambassadors to Israel while Boris Johnson said: “We understand that some have been provoking that violence but on the other hand there has got to be restraint in the use of live rounds.”
Khaled Batch, the head of the organising committee of protests, said Tuesday would be a day for funerals. It is also what Palestinians call the “Nakba” day, the anniversary of hundreds of thousands of Palestinians’ displacement following Israel’s founding.
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Palestinian president Mahmoud Abbas urged the international community to condemn what he called “massacres” carried out by Israeli troops in Gaza.
Of the 59 Palestinians killed, six were children, Gaza's health ministry said. Some 1,360 Palestinians were wounded by bullets, including 130 who were in serious or critical condition.
Egypt, an important ally of Israel, condemned the killings while the UN human rights chief, Zeid Ra’ad al Hussein, decried the “shocking killing of dozens”.
The European Union’s foreign policy chief, Federica Mogherini, called on Israel to respect the “principle of proportionality in the use of force” and show restraint, while also urging Hamas to ensure any protests remain peaceful.
Additional reporting by agencies
Welcome to our live coverage of events in Israel and the occupied Palestinian territories as fallout from the relocation of the US embassy to Jerusalem continues.
Here is our special dispatch from Gaza taking in the events of yesterday:
Israel's ambassador to the UK, Mark Regev, has said the country "did everything we could to avoid" yesterday's killings.
"We dropped leaflets urging people not to attack the border, we used social media, we used radio and television broadcasts," he told BBC Radio 4's Today programme.
"We didn't want to see this violence."
Challenged on the Israeli Defence Force's use of live ammunition, Mr Regev said protester were armed with "far more than the odd rock".
"You've got people charging the border fence with wire cutters, with explosives, with Molotov cocktails, with other weapons.
"Their goal is clear and Hamas has articulated the goal ... 'to breach the border, to get inside Israel and to kill Israeli citizens'."
Mr Regev said he "rejects" the suggestion the IDF engaged in the indiscriminate use of lethal force, as charged by Today.
The protests were not "spontaneous", he said.
He added: "If they were protesting inside Gaza no one would interfere."
Mr Regev insisted that "we only use live fire in a very measured way, a very surgical way, and only when there is no alternative".
Pressed on how so many could have died if this was the case, he said there were "40,000 people involved in violent riots on our border", with "continuous attempts" to breach the frontier.
"We have to protect our people," he added.
↵This was the White House's reaction to yesterday's killings, in which a spokesman declined to call on Israel to show restraint.
White House blames Hamas over 55 Palestinians killed by Israeli troopsThe White House has refused to condemn Israel for shooting dead at least 55 Palestinian protesters or even call for restraint, instead seeking to put the blame on Hamas and describing the protests as a “gruesome propaganda attempt”.
Rocket warning sirens sounded in southern Israel near the Gaza border on Tuesday, the Israeli military said, but it was not immediately clear whether any missiles had been fired from the Palestinian enclave.
The sirens went off on the day Palestinians mark the "Nakba", or "Catastrophe" of their dispossession when Israel was founded 70 years ago, and the day after Israeli forces killed 58 Palestinians during protests at the border.
The UN Security Council was due to meet on Tuesday to discuss yesterday's violence on the Gaza border.
Kuwait had called for the session to be held but it was unclear what might come from it.
Diplomats said countries were unable to reach unanimous agreement yesterday on a proposed joint statement circulated by Kuwait.
The draft statement would have expressed "outrage and sorrow" at the killings, sought an "independent and transparent investigation", and called on all sides to exercise restraint.
Additional reporting by AP