Israeli security guards have shot dead a Palestinian who ran towards them with a knife near Jerusalem's Old City on Tuesday, shortly after two Palestinian boys stabbed a guard on a tram nearby.

Israel and the Palestinian territories are experiencing the worst wave of violence since the 2014 Gaza war, with Palestinian militants calling for a knife "intifada", or uprising, against Israel.

Twelve Israelis have been killed since the start of October, while 73 Palestinians have been shot dead by Israeli security forces, including 44 people Israel said were carrying out attacks. Many of the assailants have been teenagers.

Police spokeswoman Luba Samri said two Palestinians, aged 12 to 13, stabbed a security guard on a light-rail train in Pisgat Zeev, a Jewish settlement north of Jerusalem. The guard shot back at them.

A hospital spokeswoman said one boy was seriously wounded. Police said the other was taken into custody. Passengers helped overcome the two youths.

A few minutes later, two security guards shot a 37-year-old Palestinian holding a knife as he ran towards.

A Palestinian bystander was wounded in the shooting.

The violence over the past six weeks has in part been fuelled by an increase in Jewish visits to a Jerusalem site that is holy to both Muslims and Jews.

In addition, Palestinians are frustrated as US-backed peace efforts have stalled and Israel's 48-year occupation of the West Bank and East Jerusalem shows no sign of ending. Gaza, ruled by Islamist Hamas which is sworn to Israel's destruction, is under a crippling Israeli-Egyptian blockade.