In the deadliest clashes in Gaza since the war in 2014, the Palestinian government says the Israeli army has killed 55 people and injured 2,700 others.
Israeli Prime Minister Benjamin Netanyahu said his troops acted to defend themselves from Islamist groups controlling Gaza, Hamas. He said the group intended to destroy Israel.
The leader of the Palestinian National Authority condemned what he called "massacre"; while the UN speaks of "excessive human rights abuses".
Violence coincided with the official opening of the United States Embassy in Jerusalem, Monday (14/05).
The inauguration sparked outrage by Palestinians as seen as US support for Israeli occupation of the entire city of Jerusalem, which the eastern part claimed Palestine as its territory and planned to become the capital of a future Palestinian state.
Israel also welcomed the 70-year-old state of Israel, established May 15, 1948 by which the Palestinian people are actually considered the day of calamity, Nakba.
What happened at the Gaza border?
Palestinians have rallied for six weeks, as part of a protest called "Great Parade to Return". The protest was led by Hamas.
However, Monday's protest - and planned on Tuesday - is the climax, marking the day of Israel's establishment in 1948 and what the Palestinians call Nakba or Malapetaka. The term refers to the hundreds of thousands of Palestinians who fled or were driven from their homes in the ensuing war.
Haris Monday also coincides with the inauguration ceremony of the US Embassy.
The Israeli military says 40,000 Palestinians participated in 'violent riots' in 13 locations along the border fence in the Gaza Strip.
Palestinians throw stones and burners while the Israeli military throws tear gas and mobilizes snipers.
Prime Minister Benjamin Netanyahu defended his military action, saying: "Every country has an obligation to protect its borders.
"The Hamas terrorist organization declared its intention to destroy Israel and send thousands of people to break through the barrier to achieve this goal and we will continue to act with determination to protect our sovereignty and our people.
An Israeli Defense Force spokesman said soldiers shot at those involved in "terrorist activities and not protesters, dissolved in ordinary ways, such as tear gas, and in accordance with the rules of engagement".
Palestinian Authority President Mahmoud Abbas announced a three-day mourning period. "Today again, the massacre of our people continues."
What is the reaction of the international community?
A number of responses that appear to be very contradictory:
White House spokesman Raj Shah said: "The responsibility for this tragic death is entirely in the hands of Hamas.. Hamas deliberately and cynically provoked this response"
EU foreign policy chief Federica Mogherini and the British government called on both sides to refrain
Germany says Israel deserves to defend itself but has to do it fairly
French President Emmanuel Macron condemned the Israeli military's violence against the protesters
Turkey says the US is also responsible for the "brutal massacre" and withdraws its ambassadors from the US and Israel
One of the strongest statements came from United Nations High Commissioner for Human Rights Ra'ad al-Hussein, who denounced "a shocking killing of dozens of people, and hundreds of people wounded by Israeli gunfire"
South Africa also recalled its ambassador to Israel, denouncing "Israel's blind and indiscriminate attack"
Is this violence linked to the opening of a new US embassy?
There was a clash between Israeli police and protesters who raised the Palestinian flag outside the new embassy in Jerusalem. Some protesters have been arrested.
Hamas said that the border rallies would indeed be stepped up on Monday and Tuesday, but President Mahmoud Abbas's response to the US Embassy move showed anger among Palestinians.
He said: "We heard today they opened the embassy, it was the occupation, not the Embassy, the US occupation in East Jerusalem."
The atmosphere at the inauguration ceremony clearly contrasts with the atmosphere on the Gaza border.
President Donald Trump sent a video message to the event, saying that Israel "has the right to determine its own capital".
Princess Trump, Ivanka, unveiled the embassy logo, and her husband, Jared Kushner, said in remarks: "When President Trump makes an appointment, he keeps it."
PM Netanyahu said: "President Trump, by recognizing history, you have recorded history."
Why is the move of the US embassy so controversial?
The status of Jerusalem is related to the core of the Israeli-Palestinian conflict.
Israel's sovereignty over Jerusalem is not recognized internationally and, according to the 1993 Israel-Palestine peace treaty, the final status of Jerusalem should be discussed at the final stages of peace talks.
Israel has occupied East Jerusalem since the Middle East war in 1967. Israel has practically annexed the territory, but it is not recognized by any country until President Trump's declaration in December 2017.
Since 1967, Israel has built dozens of settlements, home to 200,000 Jews, in East Jerusalem. The settlement is considered illegal by international law, although Israel denies it.
Countries have opened embassies in Jerusalem but many have moved after Israel passed a law formally making Jerusalem its capital in 1980.