Two Palestinian teenagers were shot dead in clashes with Israel's military on Thursday, Palestinian officials said, amid tensions over US President Donald Trump's recent Jerusalem declaration and a deadly gun attack.

Amir Abu Musaid, 16, was shot in the chest near the border fence east of Al-Bureij camp in central Gaza, the health ministry in the strip announced, following protests against Trump's controversial recognition of Jerusalem as Israel's capital.

The Israeli army said dozens of Palestinians were involved in “riots” along the border, throwing stones and burning tyres. The statement said two other Palestinians were injured in the clashes.

It said it shot at three who “put our forces in danger”.

Later another teenager was shot in the head in clashes near the city of Nablus in the occupied West Bank. Family members identified him as Ali Omar Qino, 16. Israel's army has not yet commented on the second incident.

It occurred as Israeli forces continue to search the area around Nablus after Israeli rabbi Raziel Shevah was shot dead near the city on Tuesday by unknown assailants.

Sixteen Palestinians and an Israeli have been killed since Trump's December 6 decision, which angered Palestinians who see Jerusalem as their capital.

Fourteen of the Palestinians were killed in clashes, while two were killed in an Israeli air strike on Gaza in response to rocket fire.

It was unclear whether the gun attack on the Israeli or Thursday's shooting death of the Palestinian near Nablus were related to Trump's declaration.