Israeli police officers fatally shot two Palestinians who opened fire at them outside Jerusalem's walled Old City on Sunday, police said, on a day when officials said three other Palestinian assailants were killed in two other incidents.

A police spokeswoman said two men used automatic weapons to shoot at officers stationed on the Damascus Gate plaza, a busy entrance to the Old City and the scene of many previous violent incidents, and they responded swiftly and shot the two.

Multiple rounds of gunfire could be heard on amateur video footage taken during the incident late in the evening, with traffic, including a commuter bus, stopped nearby. There were no reports of other casualties.

Earlier, the Israeli army said troops shot and killed two Palestinian teenagers who were throwing stones at cars in the occupied West Bank after coming under fire from one of them.

In a third incident, a Palestinian tried to stab an Israeli paramilitary policeman at a checkpoint in the West Bank, near Jerusalem, and was shot dead, police said.

Israeli security forces have killed at least 163 Palestinians, 107 of whom Israel says were assailants, while the others were shot dead during violent anti-Israeli protests, as the bloodshed persists into a fifth month.

Stabbings, shootings and car rammings by Palestinians have killed 27 Israelis and a U.S. citizen since early October.

As well as frustration over Jewish settlement-building, deemed illegal by the United Nations, on land Palestinians want for a state, tensions have been rising over Jerusalem's al-Aqsa mosque compound and Islamist calls for Israel's destruction.

In Sunday's shooting near the West Bank city of Jenin, "two assailants hurled rocks at cars", a military statement said. "Forces arrived and were fired upon by an assailant. Soldiers responded and shot the attackers, resulting in their deaths."

The Palestinian Health Ministry said two 15-year-old Palestinians were killed.

Wassef Abu Baker, a 56-year-old local resident, told Reuters that after hearing gunshots, he drove to within 40 meters (yards) of where one of the teenagers was lying on the ground.

"He was still moving. The soldier shouted at me to move back and they fired at him - maybe it was 12 bullets," he said.

Abu Baker said he could not see whether the person on the ground was armed. A spokesman for Israeli Prime Minister Benjamin Netanyahu tweeted a photograph of what appeared to be an M-16 assault rifle on the pavement, which he said was the weapon used against the soldiers.