A general strike was being held in both the Gaza Strip and the occupied West Bank.
"Rioters are rolling burning tyres and hurling firebombs and rocks at the security fence and at (Israeli) troops, who are responding with riot dispersal means and firing towards main instigators", it said.
Protester Saeed Juniya erected a small tent a few hundred metres from the border fence east of Gaza City, where he was accompanied by his wife and children.
He said Palestinians "expect the security council to shoulder its responsibility" and "defuse this volatile situation, which clearly constitutes a threat to global peace and security".
United Nations Secretary-General Antonio Guterres has called for an "independent and transparent investigation" after 16 Palestinians were killed and hundreds more wounded during clashes with the Israeli military, a spokesman said.
He alleged Gaza health officials exaggerated the number of wounded, and that several dozen at most were injured by live fire, with others suffering from tear gas inhalation or other types of injuries. No casualties were reported among Israelis.
The Palestinian Health Ministry says Friday's death toll in Gaza has risen to seven, with six Palestinians people killed by Israeli army fire along the border with Israel and a farmer killed by pre-dawn tank fire in a separate incident. In recent years, first Egypt and then the Palestinian Authority in the West Bank joined Israel in squeezing Gaza financially.
Israeli Ambassador Danny Danon said "the worldwide community must not be deceived" by what he termed "a well-organized and violent terror-gathering" under the banner of a peaceful march.
The military said that more than 100 army sharpshooters had been deployed in the area.
50s today, then a frigid Easter weekend
Rain will shift to the east and out of the area by noon but clouds will stick around most of the day with highs near 50. The threat of heavy rain is over, but the light rain that's fallen all afternoon has continued this evening.
The opening of the US embassy, also slated for the anniversary, is expected to add further fuel to protests.
Last Friday, Israeli soldiers opened fire at Palestinians who rallied peacefully near the border fence with Israel marking Land Day and calling for the right of return for refugees to their homes and lands in historic Palestine.
The demonstration is expected to end at the same time Washington plans to open an embassy in Jerusalem, a move that has infuriated Palestinians who have claimed the eastern section of the city as the capital of their future state.
The weekslong demonstrations, to end May 15, are created to commemorate the Nakba or "catastrophe" when hundreds of thousands of Palestinians had to flee their land or were expelled during the war in 1948 that led to the creation of Israel.
The EU is the biggest donor to the Palestinians and has spoken out against US President Donald Trump's Jerusalem decision.
Manelis said all those killed were engaged in violence.
The Israeli army, using riot control measures, injured a further 27 Palestinians in clashes in the city of Nablus as almost 900 Palestinians demonstrated in cities throughout the West Bank.
The clashes erupted in the context of what Gaza's Islamic militant Hamas rulers at promises would be peaceful protests along the Israel-Gaza border. "On the eve of Passover (of all days), which commemorates God liberating Prophet Moses and his people from tyranny, Zionist tyrants murder peaceful Palestinian protesters - whose land they have stolen - as they march to escape their cruel and inhuman apartheid bondage", Foreign Minister Mohammad Javad Zarif tweeted.
"Reports indicate that most of the demonstrators stayed well away from the border fence and were not violent", the United Nations reported Zerihoun as saying.