Israel says it has no choice but to use deadly force at the protests to defend the frontier from militants trying to destroy the barrier and infiltrate.
Weekly anti-Israel rallies and protests had been organised since the start of the marches, where Gaza health ministry officials said that over 250 Palestinians, including 47 children, were killed and around 26,000 injured.
Hassan Shalabi, 14, was killed by Israeli sniper fire to the chest at one protest site in the Gaza Strip, and Hamza Ishtiwi, 18, was hit by a fatal bullet to the neck at another demonstration, the Gaza Health Ministry said.
The Israeli army regularly arrests and shoots unarmed Palestinian fishermen, shepherds and farmers in the border areas if they near the moderation zone, as the authorities have not clarified the exact area assigned to that zone.
"They are hurling rocks at (Israeli) troops and towards the security fence, as well as a number of explosive devices that did not cross the fence", a spokesman said, adding that they had heard grenade explosions.
Tottenham vs Leicester: Mauricio Pochettino baffled by Son yellow card
Tottenham Hotspur kept their name in the hat for the title race with a hard-fought win over Leicester City at Wembley . That was after a well-worked move allowed Ricardo Pereira to drill in a cross from the right.
The military said it was aware of reports that a protester had been killed but could not confirm that the individual was a 14-year-old or what caused the death.
Israel's internal security agency says the murder of a 19-year-old Israeli woman by a Palestinian suspect near Jerusalem last week was politically motivated.
Israeli troops "responded with riot dispersal means and fired according to standard operating procedures", the spokesperson added.
Israel has fought three wars against Hamas since the miltant group took control of the enclave in 2007.
Palestinians have been holding protests every Friday since the end of last March, demanding the implementation of refugees' right of return to the lands they lost during the establishment of the state of Israel.