Two Palestinians went on a stabbing spree along a popular walkway in Jerusalem on Wednesday, killing one person, and were then shot dead by Israeli security forces in what police described as a terrorist attack.

Another Israeli was killed, apparently by police gunfire aimed at the stabbers.

A wave of violence which began almost three months ago has shown no sign of dying down and has raised fears of a wider escalation, a decade after the last Palestinian uprising subsided.

Wednesday's stabbings took place right outside the Jaffa Gate, one of the main entrances to Jerusalem's walled Old City.

"Paramilitary border policewomen saw terrorists armed with knives stabbing a man," Israeli police spokeswoman Luba Samri said. "They fired toward the terrorists and neutralized them." She added that the two Palestinians were killed.

Hospital officials said one Israeli was killed and another seriously wounded in the stabbing. A spokeswoman for Shaare Zedek Medical Center said a third person with gunshot wounds had also died. Samri said he had apparently been hurt by police gunfire at the assailants.

Police were investigating a video that surfaced on social media and appeared to show a man beating one of the shot assailants with a pole, Jerusalem police spokesman Asi Aharoni told Army Radio.

A police statement later said an initial inquiry showed the stabber was still trying to attack people even after being shot, and that the man who beat him was trying to get the knife out of his hand.

Almost daily stabbings, shootings and car-rammings by Palestinians have killed 20 Israelis and a US citizen since October. Israeli forces or armed civilians have killed at least 120 Palestinians, 72 of whom authorities described as assailants, while others died in clashes with security forces.

The surge in violence has been partly fuelled by Palestinian frustration over the collapse of US-sponsored peace talks in 2014, the growth of Jewish settlements on land they seek for a future state and Islamist calls for the destruction of Israel.

Bloodshed has also been triggered by Muslim opposition to stepped-up Israeli access to Jerusalem's al Aqsa mosque complex. The site, Islam's holiest outside Saudi Arabia, is also revered by many Jews as a vestige of their biblical temples.