A Palestinian teen from the Gaza Strip was killed east of the Burij refugee camp after a live round was fired into his chest, the Wafa news agency quoted medical sources as saying.
Three other Palestinians were wounded with one in critical condition, it said.
An Israeli military spokeswoman said “violent riots” involving rock-throwing youth erupted at two locations along the Gaza border and some 50 Palestinians were involved. Soldiers opened fire because the Palestinians “posed a threat”.
Denny Cormier, a pro-Palestinian activist who lived in Gaza during the 2014 war, wrote on Twitter that it was likely the Israeli perpetrators knew that the children did not pose a serious threat.
In the West Bank village of Iraq Burin, south of Nablus, a 16-year-old boy died at a hospital after he was shot by Israeli troops as Palestinians pelted them with stones.
Soldiers manning a checkpoint outside the village opened fire without warning, said Ghassan Daghlas, who monitors illegal Israeli settlement activities in the northern West Bank
Strict measures have been imposed on tens of thousands of Palestinians following the killing of an Israeli rabbi in a drive-by shooting in the West Bank this week.
Main roads have been closed, villages sealed off, and inspections of Palestinians increased.
The killing of the Israeli settler happened on Tuesday near the illegal Israeli settlement of Havat Gilad, where the 35-year-old rabbi resided.
Israeli settlements violate the Fourth Geneva Convention, which states that an occupying power cannot transfer its population into the territory it occupies.
Tensions in the region have increased since December, when US President Donald Trump announced that Washington recognises Jerusalem as the capital of Israel.
The status of Jerusalem has ignited tensions between Israelis and Palestinians for decades.
Israel occupied East Jerusalem at the end of the 1967 war with Syria, Egypt and Jordan; the western half of the holy city had been captured in the 1948 Arab-Israeli war.
Israel’s occupation of East Jerusalem effectively put the entire city under de facto Israeli control. Israeli jurisdiction and ownership of Jerusalem, however, is not recognised by the international community.
Palestinian leaders want East Jerusalem as the capital of their future state.