In all, 35 Palestinians were killed in the past two weeks, 28 during protests.
"The Israeli authorities must put an immediate end to the excessive and lethal force being used to suppress Palestinian demonstrations in Gaza", Amnesty International said on Friday.
Palestinians also sought to pull away barbed wire set up by Israeli forces to keep them away from the fence, an AFP journalist said.
The protest began on March 30, and is expected to culminate on May 15. But an Israeli military spokesman said the army was not involved.
A Palestinian journalist was wounded in the border clashes last Friday and later died of his injuries.
Palestinians gather to protest near the Israeli border fence, east of Gaza City in the central Gaza Strip on April. 13, 2018.
Thousands of Palestinians converged along the Gaza Strip's eastern border with Israel for the third Friday of ongoing protests against Israel's decades-long occupation.
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There have been numerous deaths among professional cyclists while competing in recent years, including others by cardiac arrest. I'm exhausted after this race but not as exhausted as in previous years, when I didn't win it for some reasons, " Sagan said.
Protesters want refugees to be allowed to return to ancestral land now in Israel.
The Israeli army said some demonstrators on Friday repeatedly attempted to destroy obstacles that the army had erected. The rioters also threw explosives and rocks toward the Israeli side of the border and attempted to fly a kite over to the Israeli side that had a firebomb attached to it.
Gaza's Health Ministry said more than 1,300 Palestinians were wounded by live fire in the past two weeks. "An order to open live fire at unarmed protesters is manifestly unlawful", it said. Hamas official Mohammed Thuraya said, "This is our duty to our people, to ease the suffering of our citizens".
But Palestinians say protesters are being shot while posing no threat to soldiers, and United Nations Secretary-General Antonio Guterres and the European Union have called for an independent investigation. At least 26 were killed during protests. Protesters stuck a Palestinian flag into the fence and affixed a rope, using it to tug at the coils.
Israeli troops shot and wounded 30 Palestinians during a protest on the Gaza-Israel border yesterday in which demonstrators hurled stones and burned tyres near the frontier fence, Palestinian medics said.
No Israelis have been killed during the protests.