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"
- 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"