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Fresh protests against Israel are expected in the Palestinian territories, a day after Israeli troops killed 55 people in the Gaza Strip.
Tuesday marks the 70th anniversary of what Palestinians call the Nakba, or Catastrophe, that saw thousands flee amid the creation of Israel in 1948.
Tensions will be high in Gaza where those killed on Monday will be buried.
The violence came as the US completed the move of its embassy to Jerusalem from Tel Aviv, incensing Palestinians.
They claim East Jerusalem as the capital of a future Palestinian state and see the US move as backing Israeli control over the whole of the city - which Israel regards as its indivisible capital.
Palestinian officials said that, as well as those killed, about 2,700 people were injured in Monday's violence - which they condemned as a massacre. It was the deadliest day in Gaza since the 2014 war.
Israeli PM Benjamin Netanyahu said his military was acting in self-defence against Gaza's Islamist rulers, Hamas, who he said wanted to destroy Israel.
What happened at the Gaza border?
Palestinians were demonstrating on Monday as they have been for six weeks as part of a protest, orchestrated by Hamas, called the "Great March of Return".
However, Monday's protests - and those planned for Tuesday - are the culmination as they mark the anniversary of Israel's creation in 1948 and commemorate the hundreds of thousands of Palestinians who subsequently fled their homes or were displaced in the war that followed.
Monday also coincided with the dedication ceremony for the US embassy.
Israel said some 40,000 Palestinians had taken part in "violent riots" at 13 locations along the Gaza Strip security fence.
Palestinians hurled stones and incendiary devices, while the Israeli military used tear gas and live fire from snipers.
Mr Netanyahu defended his military, saying: "Every country has an obligation to defend its borders.
"The Hamas terrorist organisation declares its intention to destroy Israel and sends thousands to breach the border fence in order to achieve this goal. We will continue to act with determination to protect our sovereignty and our citizens."
An Israel Defense Forces (IDF) spokesman said soldiers had fired on those engaged in "terrorist activity and not on demonstrators, who were dispersed by usual means such as tear gas and according to the rules of engagement".
Announcing three days of mourning, Palestinian Authority President Mahmoud Abbas said: "Today once again, the massacres against our people continue."
What has the international reaction been?
There has been fierce condemnation from some countries, but Israel's key ally, the US, has backed it:
White House spokesman Raj Shah said: "The responsibility for these tragic deaths rests squarely with Hamas... Hamas is intentionally and cynically provoking this response"
Kuwait drafted a UN Security Council statement calling for an independent inquiry into the violence - and expressing "outrage and sorrow" - but this was blocked by the US
The UK said "the large volume of live fire is extremely concerning" but said protests must be peaceful
Germany said Israel had the right to defend itself but should do so proportionately
France's President Emmanuel Macron condemned violence by the Israeli military
Turkey said the US shared responsibility with Israel for a "vile massacre" and that it was recalling its ambassadors from both countries
One of the strongest statements came from UN human rights chief Zeid Ra'ad al-Hussein, who condemned the "shocking killing of dozens, injury of hundreds by Israeli live fire"
South Africa also recalled its ambassador to Israel, condemning "the indiscriminate and grave manner of the latest Israeli attack"
Was the violence linked to the opening of the embassy?
The protests were scheduled as part of the Great March of Return and Hamas had said they were being stepped up for Monday and Tuesday in any case.
But the highly controversial US embassy opening in Jerusalem galvanised Palestinian demonstrators.
Mr Abbas called the new embassy "a US settlement in East Jerusalem".
Why is the embassy move so controversial?
The status of Jerusalem goes to the heart of the Israeli-Palestinian conflict.
Israeli sovereignty over Jerusalem is not recognised internationally and, according to the 1993 Israel-Palestinian peace accords, the final status of Jerusalem is meant to be discussed in the latter stages of peace talks.
Israel has occupied East Jerusalem since the 1967 Middle East war. It effectively annexed the sector, though this was not recognised by any countries until Mr Trump's declaration in December 2017.
Since 1967, Israel has built a dozen settlements, home to about 200,000 Jews, in East Jerusalem. These are considered illegal under international law, although Israel disputes this.
Various countries once had embassies based in Jerusalem but many moved after Israel passed a law in 1980 formally making Jerusalem its capital.