The Israeli military claimed that the boys were involved in planting an explosive device adjacent to the fence.
Israeli Prime Minister Benjamin Netanyahu has said he welcomes mediation from the United Nations and Egypt to prevent a humanitarian collapse in the Gaza Strip, Israeli media said Tuesday.
The teens' bodies were wrapped in Palestinian flags and carried by mourners who shot in the air as they chanted "God is great".
However, their parents said they were having fun and laying a bird trap in the area.
Ibrahim al-Satari, the father of 13-year-old Mohammed, said he couldn't understand it.
The incident occurred with tensions high along the border after months of protests and clashes. Later, he said, "I heard the explosion and I knew they were dead". Islamic Jihad, which sometimes acts independently from Hamas, was behind the latest rocket fire into Israel, which it said was in retaliation for the killing of four Palestinians during a Friday protest along the boundary fence. "These are small children", he said.
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The Frenchman was renowned for playing youth in the competition, and despite getting to the final, was never able to lift the trophy.
Israel and Palestinian militants in Gaza have fought three wars since 2008 and the recent unrest has raised fears of a fourth.
Thousands gathered Monday on the beach for a Hamas-led protest against the blockade.
Palestinians and rights groups say protesters have been shot while posing little threat.
Since last March, under the banner of a peaceful march to express their yearning to see the destruction of Israel so they could return to homes they had never actually seen, Arab mobs have assaulted Gaza's border fence with Israel and IDF soldiers on the other side, resulting in bloody clashes. Most also blame Hamas, the Palestinian Authority in Ramallah, or the UN-not Israel-for their severe economic woes.
Israel accuses Hamas of using the large protests as cover to stage border infiltrations and attacks.
The World Health Organization (WHO) issued a special situation report, which showed that 14 Palestinians, including four children, were killed and 1,434 were injured by the Israeli forces in the past two weeks in Gaza.