"Any Israeli assault on the marches will be met with an equal response", the Islamic Jihad said following a meeting between group chief Jihad al-Nakhla and Hamas deputy leader Saleh al-Aarouri in Lebanese capital Beirut.
The protesters waved Palestinian flags and held signs in support of the Palestinian right of return while chanting against the 11-year blockade of the strip.
The protesters threw stones at the Israeli soldiers and burnt tires.
Israel reopened its crossings with the blockaded Gaza Strip on Sunday after having kept them closed for almost a week following a rare long-distance rocket strike from the Palestinian enclave, an official said.
The Israeli military says Hamas used restraint during protests at the Israel-Gaza border; Trey Yingst reports from Gaza City.
Israeli forces relied on tear gas, but utilized live fire in some instances, killing four terrorists.
Since the first Great March of Return rallies, Israeli forces have killed almost 300 Palestinians in Gaza, 200 of them during unarmed protests, according to the Gaza-based human rights group Al Mezan.
Netanyahu said the Israeli military's massive deployment had ensured violence at the protests remained relatively low.
Guardiola hails City's positive mind-set
But AGUERO did it in 46 fewer games. "We are realistic", said Fulham caretaker boss Scott Parker. 'They could. But this team is prepared to withstand the pressure, I'm sure of that.
Hamas, the Islamist group prominent in the Gaza Strip, told the BBC it would try to keep Saturday's protests peaceful and a safe distance from the fence, as Egyptian and United Nations mediators tried to prevent escalation.
The clashes appear at present to be limited in scope and fears of a large number of deaths have so far not materialised.
The protests came on the heels of a week in which rockets were launched from Palestine into Israel and the Israeli military retalited with bombings of Gaza.
In another sign of the confrontation easing - as Egyptian mediators pushed on for a full ceasefire - Palestinians said Israel would on Monday nearly double the breadth of Mediterrean waters where they are permitted to fish.
Earlier this month, Hamas violently suppressed several days of public protests, staged under the slogan "We want to live", over the dire conditions.
The army also said it caught two young Palestinian children who had tried to cross the border with a knife.
Three Palestinians were killed and hundreds injured as thousands protested in Gaza to mark Land Day and the one-year anniversary of the Great March of Return protests.
"This was not something extraordinary, and much, much, much less than what people were anxious about", retired Israeli Brig. He said he plans to show his children the Israeli soldiers and return to safety before the march started.
Unless undertaken lawfully in self-defence, intentionally shooting a civilian not directly participating in hostilities is a war crime.