Mourners carry the body of Huzeifa Othman Suleiman, an 18-year-old Palestinian man who was shot dead by Israeli soldiers during clashes the previous day in Tulkarem, during his funeral.
Ramallah - Israel's army shot dead the 13-year-old Palestinian during clashes at a refugee camp near Bethlehem.
New clashes erupted on Monday in the West Bank and east Jerusalem while Israel's military shot dead a 13-year-old Palestinian after Prime Minister Benjamin Netanyahu pledged a crackdown following attacks that killed four Israelis.
The spike in violence has led to international calls for calm, with concerns the unrest could spin out of control and memories of previous Palestinian uprisings still fresh.
As part of security measures following the recent attacks, Jerusalem's Old City remained closed to Palestinians for a second straight day.
On Monday afternoon, Israel's army shot dead the 13-year-old Palestinian during clashes at a refugee camp near Bethlehem, police and emergency services said.
The teen was hit in the chest, making him the second Palestinian killed by Israeli fire in 24 hours. Dozens of others have been wounded.
An Israeli army spokeswoman said some 50 rioters were hurling stones at security forces and "on the continued aggression, the force responded with 0.22-calibre rounds at the main instigators, identifying a hit."
"It will be investigated and we are aware of reports regarding a dead Palestinian," the spokeswoman said.
Further clashes between soldiers and protesters later occurred inside Bethlehem as well as in Shuafat in east Jerusalem.
Video purportedly showing Israeli police shoot dead a 19-year-old Palestinian accused of stabbing a 15-year-old early on Sunday has added to tensions, with the man's family accusing security forces of executing him.
Palestinian youths throwing stones and firebombs have faced off against Israeli security forces using both live rounds and rubber bullets. Jewish settlers have also clashed with Palestinians.
The rioting has followed attacks in recent days that have killed four Israelis and wounded several others, including a two-year-old child.
Late on Sunday, Netanyahu pledged "a fight to the death against Palestinian terror" after meeting security chiefs and announced a package of new measures.
They included swifter demolition of the homes of those accused of attacks, broader use of detention without trial for suspects, and police and troop reinforcements for Jerusalem and the West Bank.
Palestinian president Mahmoud Abbas, who said in a UN speech last week that he was no longer bound by previous accords with Israel, accused Netanyahu's government of escalating tensions.
It was not clear what Abbas's UN declaration would mean in practice, including whether he would act to end security cooperation with Israel.
European nations and the United States have appealed for calm, with Germany warning of the risk of a "new intifada".
In a rare and drastic move, Israel barred Palestinians from Jerusalem's Old City on Sunday after two Israelis were stabbed to death there. The neighbourhood remained mainly quiet early Monday, with hundreds of police on patrol.
The Old City restrictions are to be in place through Monday, when Jews wrap up celebrations of the eight-day Sukkot holiday. Only Israelis, tourists, residents of the area, business owners and students were allowed in.
Worship at the sensitive Al Aqsa mosque compound has been limited to men aged 50 and above. There were no age restrictions on women.
Around 300,000 Palestinians live in Israeli-annexed east Jerusalem, where the Old City is located.
"These people were stabbed just for being Jews, but that will keep no one from going about their lives," said Shilo Marom, a 25-year-old on his way to pray at the Western Wall, where dozens of Jews could be seen Monday morning marking the last day of Sukkot.
Esraa Hajajra, 19, was among several Muslims protesting at one gate over limited access to the Al Aqsa compound.
"This is our mosque, but they want to take it and pray there," she said, referring to suspicions among Palestinians that Israel will seek to change rules governing the compound, which Netanyahu strongly denies.
The mother (C) of Huzeifa Othman Suleiman, an 18-year-old Palestinian man who was shot dead by Israeli soldiers during clashes the previous day in Tulkarem, is comforted by relatives during the funeral of her son.