Israel said its troops had shot a group who broke through the fence with a bomb and attacked an army post.
In response to the violence, Israeli Defence Minister Avigdor Lieberman ordered deliveries of fuel to the Palestinian enclave be suspended.
Seven Palestinians died Friday after being shot by Israeli soldiers along the security fence between Gaza and Israel during violent weekly protests, according to the Palestinian Ministry of Health.
The P.A., controlled by the Fatah Party, is engaged in a long-standing rivalry with the Hamas, which controls Gaza and has slashed salaries to public servants in Gaza by as much as 30 percent.
Protesters have sent incendiary devices attached to balloons into Israeli territory during demonstrations, which Israel says has caused hundreds of thousands of dollars-worth of damage to farmland. They also seek the right to return to lands that Palestinians fled or were driven from upon Israel's founding in 1948.
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A spokesman for the Palestinian health ministry said six Palestinian men were killed as thousands of protesters approached the heavily-guarded Israeli border.
Palestinians gather at the Israel-Gaza border fence during a protest calling for lifting the Israeli blockade on Gaza and demanding the right to return to their homeland, in southern Gaza on October 12, 2018.
There had been hopes the protests would ease after the UN-brokered agreement to ease the strip's energy crisis took effect this week.
Hamas' chief, Ismail Haniyeh, who attended a protest in east Gaza City, said that "the determination of the Palestinian people will break the siege".
Hamas had seized control of Gaza from Western-backed Palestinian President Mahmoud Abbas in 2007 and has since fought three wars with Israel, most recently in 2014.