Unrest returned to Jerusalem Tuesday after a lull of more than a week with two knife attacks, one near the Old City and another by alleged assailants aged 12 and 14.
There was also a knife attack in the West Bank and, in a separate incident, a failed stabbing attempt.
The latest violence came a day after Israeli Prime Minister Benjamin Netanyahu met US President Barack Obama for talks in Washington that included discussions on a wave of violence that began in October.
In one of the two Jerusalem attacks, a knife-wielding Palestinian ran towards two security guards near the Damascus Gate, a main entrance to the Old City, and the guards shot him, police said.
The man, named as Mohammed Nimr, 37, from the east Jerusalem neighbourhood of Issawiya, died of his wounds in a Jerusalem hospital.
In the east Jerusalem Israeli settlement of Pisgat Zeev, two Palestinian boys aged 12 and 14 attacked a security guard with knives, police said.
The younger of the boys, both from Jerusalem's Shuafat refugee camp, was shot and seriously wounded and the other was arrested.
The security guard was moderately injured, police spokeswoman Luba Samri said.
In a third incident, just outside Israeli-annexed east Jerusalem, a Palestinian tried to stab a border policeman near the West Bank village of Abu Dis and was killed by security forces, police said.
While knife and car-ramming assaults have continued in the occupied West Bank amid a weeks-long surge of violence, Tuesday's attacks were the first in Jerusalem in more than a week.
The unrest has seen 10 Israelis and at least 77 people on the Palestinian side -- one of them an Israeli Arab -- killed since October 1. Many of the Palestinians killed were alleged attackers.
On Tuesday, Palestinians in the southern West Bank city of Hebron demonstrated to demand that Israel give up for burial the bodies of dead Palestinians it is withholding.
Israeli authorities are retaining about 20 corpses in a policy meant to discourage attacks and stop funerals from becoming political rallies likely to further inflame emotions.
A large number of the attacks have been carried out by young Palestinians.
- 'Did not intend to kill' -
A 13-year-old Palestinian went on trial on Tuesday charged with attempted murder after two Israelis were stabbed and seriously wounded in occupied east Jerusalem last month.
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One of the victims, a 13-year-old who was riding his bicycle, was critically wounded but is recovering in hospital.
The incident, on October 12 in Pisgat Zeev, involved not only Ahmed Manasra, but also his 15-year-old cousin, Hassan.
Ahmed was hit by a car as they fled, and Hassan was shot dead by Israeli security forces when he allegedly threatened them with a knife.
Footage released by Israeli authorities in the wake of the attack purported to show the cousins -- knives in hand -- following the Israeli victims.
Ahmed's Israeli lawyer Lea Tsemel entered a plea of not guilty, saying that he had no intent to kill.
"He did not intend to kill anyone," she told AFP at the courthouse.
"He wanted to frighten them, to show them that they cannot keep killing (Palestinians) without a reaction."
Leaked video of an interrogation posted by Palestinian media purportedly shows him in tears as an Israeli officer shouts and shakes his fist at him while making him watch CCTV footage of the attack.
"Look you liar, it's you," the man says in Arabic.
"I don't know, I don't remember," Manasra says. "Everything you say must be true."
Another of his lawyers, Palestinian Tariq Barghout, said the seven-minute clip was a "compilation" of moments from the full 4.5-hour interrogation, which he said he had viewed.
He told AFP that he was not the source of the clip and it was unclear who leaked it.
Reacting to the video, police spokeswoman Samri said the questioning was carried out "in a professional manner".
"We are talking here of a terrorist accused of trying to kill innocent people," she told AFP.
In Monday's first meeting between Netanyahu and Obama in more than a year, the Israeli premier reiterated his commitment to a two-state solution to the conflict after being heavily criticised for previously sending mixed signals on the issue.
Obama and Netanyahu stressed close US-Israeli ties during the tightly choreographed White House appearance designed to quiet disputes over Iran and Middle East peace.