Two Palestinians have been shot and killed in separate incidents after they allegedly attempted to stab Israeli personnel near Jerusalem's Old City and in the occupied West Bank, Israeli officials have said.

Two Israeli security guards shot a Palestinian holding a knife as he ran towards them, Luba Samri, an Israeli police spokesperson, said on Tuesday.

The hospital where the 37-year-old was taken said he later died of his wounds. An Israeli security guard suffered moderate injuries. A Palestinian bystander was also wounded in the shooting, Samri added.

In a second incident, a Palestinian who allegedly attempted to stab an Israeli border policeman near the occupied West Bank village of Abu Dis was shot dead. The incident occurred in an area adjacent to Israeli-annexed East Jerusalem.

In a separate incident, Samri said two Palestinian boys, ages 12 and 13, allegedly stabbed a security guard on a light rail train in Pisgat Zeev, a Jewish settlement north of Jerusalem.

One of the two boys was injured severely after being shot by the guard. Police said the second boy was taken into custody. 

Israel and the Palestinian territories are experiencing the worst wave of violence since the 2014 Gaza War.

Ten Israelis have been killed since October 1, while 80 Palestinians have been shot dead by Israeli security forces, including 44 people whom Israel claimed were carrying out attacks. 

The violence over the past six weeks has, in part, been fuelled by an increase in Jewish visits to the Al-Aqsa Mosque compound in East Jerusalem, a site holy to both Muslims and Jews.

Source: Al Jazeera and agencies