Numbers were down from the previous Friday, when tens of thousands approached the border in demonstrations that saw Israeli forces kill 19 Palestinians, making it the bloodiest day in Gaza since a 2014 war.
Thousands of protesters approached the border fence around Gaza for a second Friday in a row, burning tires and hurling stones at Israeli forces, who responded with tear gas and live ammunition.
The report further referred to concerns by the Israeli army sources that in case of many Palestinian casualties, the global community might renew diplomatic pressure on the regime.
"France reminds the Israeli authorities of their duty to protect civilians and urges them to show the greatest restraint", a Foreign Ministry spokeswoman said in a statement according to Reuters.
"We stand in solidarity with the Israelis who have taken to the streets this last week to protest their government's actions", he said. Nine Gazans were killed and over 1,000 wounded in the day's clashes.
Palestinian paramedics set up medical posts ahead of Friday's rallies, as more than 1,500 demonstrators were injured during last week's protests - half of them by live fire.
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Once a location is agreed upon the officials said that the date will be set and the agenda discussed in greater detail. South Korea brought Kim's offer to meet to the White House last month, which Trump reportedly expected on the spot.
The Israeli military accused the "approximately 10,000 Palestinians" who attended of "rioting in five locations along the border with the Gaza Strip".
The report added that 14 other journalists were arrested, briefly detained or were shot at by Israeli soldiers but fortunately uninjured. The wounded Palestinian was taken to hospital in serious condition.
Earlier on Friday, the United Nations human rights office deplored the reported use of "excessive force" by Israeli soldiers during the March 30 protests in Gaza, where at least 16 people were killed and more than 1,000 others injured.
Israeli Prime Minister Benjamin Netanyahu addressed the riots on the Gaza border over the last few weeks on Saturday, saying.
On Saturday, the European Union raised questions over whether Israeli troops engaged in "proportionate use of force".
Tension has grown across the Palestinian territories since December 6 when U.S. President Donald Trump officially recognized Jerusalem as the capital of Israel.
In the West Bank political capital of Ramallah, around 50 Palestinian journalists held a vigil for Murtaja.