RAMALLAH - Fresh clashes erupted Monday in the West Bank and Israel's military shot dead a 13-year-old Palestinian boy after Prime Minister Benjamin Netanyahu pledged a crackdown following attacks that killed four Israelis.

The spike in violence in the West Bank and east Jerusalem 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. The teen was hit in the chest, making him the second Palestinian killed by Israeli fire in 24 hours, but further details of the incident were unclear.

On Sunday night, an 18-year-old Palestinian was killed during clashes in Tulkarem in the West Bank. Dozens of others have been wounded. "He is not the first martyr, nor will he be the last, but he died for his homeland," his father Othman Suleiman told AFP at his son's funeral on Monday, attended by hundreds.

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 three attacks in recent days that have killed four Israelis and wounded several others, including a two-year-old child. Late Sunday, Netanyahu pledged "a fight to the death against Palestinian terror" after meeting security chiefs immediately following his return from the United States.

Netanyahu, facing pressure from right-wing members of his governing coalition to respond forcefully, announced a package of new measures "to prevent terror and deter and punish the attackers".

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. He also spoke of using restraining orders to keep "inciters" away from the flashpoint Al-Aqsa mosque compound, the site of repeated clashes in recent weeks.

Palestinian president Mahmud Abbas, who said in a UN speech last week that he was no longer bound by previous accords with Israel, accused the Israeli 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.

In a rare and drastic move, Israel barred Palestinians from Jerusalem's Old City on Sunday as violence spread after two Israelis were stabbed to death. 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. "There is a concern among people (that there will be more attacks)," 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.

"These people were stabbed just for being Jews, but that will keep no one from going about their lives."

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.

Israeli security forces were already on alert after recent clashes at the compound and surrounding Old City, as well as the murder in the West Bank of a Jewish settler couple in front of their young children on Thursday.

On Saturday night, a 19-year-old Palestinian said to be a man killed two Israelis in the Old City and wounded a child, prompting a further security clampdown.

In a separate incident early Sunday, a 19-year-old Palestinian stabbed and wounded a 15-year-old passerby in west Jerusalem before being shot dead by police while fleeing.

Video circulated on social media showed what appeared to be the alleged attacker walking as bystanders shouted "shoot him" in Hebrew before a policeman fired and he fell to the ground.

Meanwhile, Germany voiced concern Monday about the risk of a "new intifada" following clashes in Jerusalem, three days ahead of a Berlin visit by Israeli Prime Minister Benjamin Netanyahu.

"What possibly awaits us here is something like a new intifada," said foreign ministry spokesman Martin Schaefer. "That can't be in anyone's interest - it can't be something anyone in Israel wants, or which any responsible Palestinian politician wants. "That's why it is... so important to search for ways and means to resume talks in order to reach a permanent solution."

Schaefer said Berlin was "seriously concerned about the escalation of violence that has claimed several lives again in Jerusalem and the West Bank at the weekend". "We condemn in the strongest terms the abhorrent knife attacks on Israeli bystanders in Jerusalem on Friday" which had killed two people and wounded three, he said.