A 16-year-old died in an exchange of fire with troops carrying out an arrest raid outside the northern city of Nablus, the Palestinian health ministry and Israeli security forces said.
Separately, a Palestinian in his 20s was killed in Qalandia outside Jerusalem, the health ministry said.
Teenager Nader Haitham Rayan died in Balata camp near Nablus after being hit by bullets to the head, chest and hand, the ministry said. It did not give further details on the circumstances of his death.
A spokesman for Israel's border police said a Palestinian had been killed.
"A terrorist fired at our troops who responded and killed him," he said.
The exchange of fire came as Israeli troops were leaving the camp after arresting a Palestinian fugitive wanted for alleged terrorism offences.
"Just as they were preparing to exit the camp, a terrorist arrived on a motorbike and fired towards them," the spokesman added.
Rayan's body was wrapped in a Palestinian flag ahead of his burial on Tuesday, during which gunmen fired into the air.
The Palestinian health ministry said another nine people were wounded in the exchanges, one of them seriously.
The second death occurred in Qalandiya, a town on Jerusalem's northern outskirts that hosts the main checkpoint between annexed east Jerusalem and the northern West Bank.
Alaa Shaham, in his 20s, was killed by a "live round to the head", the ministry said.
US envoy visits
Commenting on the violence in Qalandia, the border police said riots erupted when forces entered the area to arrest "two people involved in terrorist activities".
"Hundreds of rioters threw heavy objects from the roofs of houses endangering Israeli forces" who fired in response, a statement said, without mentioning the reported fatality.
Hundreds gathered for Shaham's funeral, including gunmen from the Al-Aqsa Martyrs' Brigade, the armed wing of Palestinian president Mahmud Abbas's Fatah faction.
Palestinian authorities said the two deaths brought to 20 the number of Palestinians killed by Israeli forces this year.
With violence flaring in the West Bank, US deputy assistant secretary of state Hady Amr was in the region for a tour aimed in part at trying to "reduce tensions", a US embassy spokesperson said.
Hadr is also seeking "to implement specific economic steps that will improve lives", the spokesperson added.
Israeli Prime Minister Naftali Bennett, who opposes Palestinian statehood, has ruled out formal peace talks with the Palestinians during his tenure but has said he is committed to expanding economic opportunities in the West Bank.
Israeli officials have said they are specifically seeking to ease tensions ahead of the Muslim holy month of Ramadan, which begins next month.
During Ramadan last year, clashes across east Jerusalem and the West Bank partly triggered an 11-day war in Gaza between Israel and armed Palestinian groups.
Israeli Foreign Minister Yair Lapid met Jordan's King Abdullah II last week to discuss maintaining calm through Ramadan and the Jewish holiday of Passover, which this year overlaps with the Muslim holy month.
