By Jeffrey Heller

JERUSALEM (Reuters) - Violence intensified in Jerusalem and the West Bank on Sunday after Israelis were targeted in two stabbing attacks and a Palestinian was killed in a clash with Israeli troops, officials said.

A Palestinian man stabbed and wounded an Israeli teenager in Jerusalem, 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.

Later in the day, an 18-year-old Palestinian was shot and killed during a clash with Israeli forces in the occupied West Bank town of Tulkarm, hospital officials said. The Israeli military said it was looking into the report.

Prime Minister Benjamin Netanyahu met security chiefs on Sunday to discuss more action to tackle rising violence in East Jerusalem, which includes the Old City, and the West Bank, areas that Israel captured in a 1967 war.

In broadcast remarks, Netanyahu said the new measures would include speeding up the razing of homes of Palestinian attackers and banning those who incite violence from the Old City.

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 uprisings.

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.

Islamic Jihad later said the attack was carried out by one of its members.[ID:nL5N1230QH] Its al-Quds Brigades said the fatal stabbing was a "heroic attack" in response to "continued Zionist aggression" at Islamic holy sites.

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In violence in another West Bank city called Jenin, 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.

Violence also erupted in the south when Palestinian militants in the Gaza Strip fired a rocket into Israel, causing no injuries or damage. Israel usually retaliates for such attacks with air strikes in Gaza.

Tensions have been further 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 has frequently banned young Muslim men from entering the area on security grounds.

Israeli-Palestinian peace talks collapsed in 2014.

(Additional reporting by Maayan Lubell in Jerusalem and Ali Sawafta in Ramallah; Editing by Jon Boyle and Eric Walsh)