On Monday, 58 people were killed when Israeli troops opened fire during Palestinian protests.
Tuesday is the 70th anniversary of what Palestinians call the Nakba - a mass displacement after Israel's creation.
Israel's military said it was preparing for further confrontations on Tuesday ,but Palestinian groups indicated they intended to rein in the protests.
Monday's violence came as the US inaugurated its first embassy in Jerusalem, a controversial move that broke with decades of US policy and incensed Palestinians.
Palestinians claim East Jerusalem as the capital of a future Palestinian state. Many 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 had been injured in what they called a massacre.
Israeli Prime Minister Benjamin Netanyahu said his military was acting in self-defence against Gaza's Islamist rulers, Hamas, who seek to destroy Israel.
Israel's military said it had only fired at "targets of terrorist activity".
The UN human rights office was heavily critical of Israel's use of force.
"The mere fact of approaching a fence is not a lethal, life-threatening act, so that does not warrant being shot," spokesman Rupert Colville told reporters in Geneva.
"How much threat can a double amputee be making from the other side of a large fortified fence?" he asked - referring to a widely shared report that a wheelchair user was killed during the violence.
Israel said some 40,000 Palestinians had taken part in "violent riots" at 13 locations along Israel's security fence on Gaza's eastern border on Monday.
Palestinians hurled stones and incendiary devices and approached the border fence. Israeli snipers fired live ammunition at protesters and used tear gas dispersed from drones.
Palestinians were demonstrating as they have been for seven weeks, as part of a protest branded the "Great March of Return".
Monday's protests were timed to mark the anniversary of Israel's creation in 1948 and the hundreds of thousands of Palestinians who subsequently fled their homes or were displaced in the war that followed.