A Palestinian knifed an Israeli to death in the occupied West Bank on Monday and in Jerusalem two Palestinian girls stabbed an elderly man with scissors before a policeman shot them both, killing one, a surge of attacks that stirred U.S. consternation.

In a day of rapidly unfolding violence, the latest in an eight-week wave of stabbings, shootings and car rammings, a Palestinian was also shot dead near the West Bank city of Nablus after approaching Israeli troops with a knife, the army said.

The Palestinian who fatally stabbed the Israeli was also shot dead.

U.S. Secretary of State John Kerry, scheduled to meet on Tuesday with Israeli and Palestinian leaders at loggerheads since their peace negotiations under his auspices stalled in April 2014, was circumspect about his latest mission.

"This is an effort to see if we can get some concrete steps in place - begin to build them, maybe - that could calm things down a little bit so people aren't living in absolute, daily terror that they might be stabbed or driven into or shot trying to walk around their city," he said during a visit to Abu Dhabi.

"It happens almost every day over there and it's terrible, and too many Israelis have been killed and stabbed, and too many Palestinians," Kerry told reporters. "And there's no excuse for any of the violence."

Eighty-six Palestinians have been killed since Oct. 1, some while carrying out attacks and others in clashes with Israeli forces. Palestinian attacks have killed 20 Israelis and an American.

It is the worst unrest since last year's Gaza war, prompting talk of a new Palestinian uprising, or Intifada, against Israel. The first intifada lasted from 1987-1993 and the second from 2000-2005, although both were far more intense and deadly.

"NO MOOD FOR CONCESSIONS"

Kerry said Washington was "perfectly prepared to work and (has) ideas for how things could proceed" to stem the bloodshed. But he cautioned: "People aren't in the mood for concessions."

At the petrol station in the West Bank, on the side of a road regularly used by Israelis to drive between Jerusalem and Tel Aviv, a Palestinian stabbed two Israelis, killing one of them, before he was shot dead by soldiers.

The Palestinian health ministry said the Palestinian shot dead near Nablus was 16. It said a Palestinian woman, 18, was critically hurt in the incident, but had no further details.

The attack in Jerusalem occurred on Jaffa Road, a busy downtown street near a market. Two Palestinian girls, one aged 14 and the other 16, used scissors to stab and slightly wound a 70-year-old man, who turned out to be Palestinian, not Israeli.

Closed circuit television footage showed the girls, their right arms raised and making stabbing gestures, advancing on the sidewalk toward a man who then appeared to draw a handgun.

Another man, identified by police as a bomb disposal officer, ran in with pistol drawn. He fired at the 14-year-old, who fell to the ground just as a third man hit her with a chair.

The officer then discharged his gun several times at the older girl, who crumpled against a wall. He ran back to the first teen, who was lying motionless on the ground, and fired at her again. A ricochet injured a Israeli passerby, medics said.

The Palestinian government has said Israel is carrying out unlawful killings of Palestinians and "accusing every victim of holding a knife" or planting knives on alleged attackers.

Last month, a U.S. State Department spokesman said that while Israel had a right and responsibility to protect its citizens, he cited reports "of what many would consider excessive use of force". Israel bristled at those remarks, saying shooting attackers was self-defense.

The bloodshed has been driven in part by Muslim agitation over stepped-up Jewish visits to East Jerusalem's al Aqsa mosque compound - Islam's third holiest site and also revered by Jews as the location of two destroyed biblical temples.