By Jeffrey Heller
JERUSALEM (Reuters) - A Palestinian man stabbed and wounded an Israeli teenager in Jerusalem on Sunday, just hours after another knife-wielding attacker killed an off-duty Israeli soldier and a rabbi nearby in the walled Old City, police said.
Officers shot dead both attackers, a police spokesman said, and Israel's government announced it was barring Palestinians from entering the ancient district for two days, apart from people who lived there.
Prime Minister Benjamin Netanyahu's office said he would meet security chiefs later on Sunday to discuss more action to tackle a rising wave of violence in East Jerusalem, which includes the Old City, and the West Bank, areas that Israel captured in a 1967 war.
The bloodshed - which included a drive-by shooting that killed an Israeli couple in the West Bank on Thursday and an arson attack that killed a Palestinian toddler and his parents in July - has triggered concerns of wider escalation.
Israel's best-selling newspaper, Yedioth Ahronoth, published a banner front page headline reading "The third Intifada", though the violence has not reached the levels of past Palestinian intifadas or uprisings.
A Palestinian man stabbed and wounded a 15-year-old Israeli in Jerusalem early on Sunday, police said. A policeman shot him dead, in a confrontation captured on amateur video shown on Israeli news sites.
On Saturday, another Palestinian stabbed to death an off-duty Israeli soldier walking with his wife and children and a rabbi who rushed to their aid, on a street near Judaism's Western Wall, police said.
Israeli police fatally shot the assailant, later claimed by Palestinian militant group Islamic Jihad as a member.
Islamic Jihad's al-Quds Brigades described Saturday's fatal stabbing as a "heroic attack" in response to "continued Zionist aggression" at Islamic holy sites.
In violence in the West Bank city of Jenin on Sunday, Israeli forces on a raid to arrest "wanted men involved in terrorist activities" were confronted by a crowd of Palestinians that threw explosives at them, the army said.
A local hospital director said 22 Palestinians were wounded by live ammunition.
Tensions have also been inflamed by frequent clashes between Palestinian rock-throwers and Israeli security forces at Jerusalem's al-Aqsa mosque compound.
Palestinians have said they fear increasing visits by Jewish groups to al-Aqsa compound, revered by Jews as the site of Biblical temples, are eroding Muslim religious control there.
Israel has pledged to maintain Muslim prayer rights at al-Aqsa, but, citing security concerns, has frequently banned young Muslim men from entering the area.
Israeli-Palestinian peace talks collapsed in 2014.