The Palestinian was stopped by a neighbour, an off-duty Israeli soldier, who shot him, the official said.
Palestinian President Mahmoud Abbas, meanwhile, announced he was suspending contact with Israel on "all levels", dealing a blow to recent USA attempts to renew the long-dormant Israeli-Palestinian peace talks.
"I condemn Israel's insistence on its position despite all warnings. and the excessive use of force by Israeli forces against our brothers gathered for Friday prayers", he said in a statement.
The deadly attack took place after three Palestinians were killed by Israelis during violent clashes on Friday.
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Bicking said he favored a policy in which there would be less officer discretion for when the cameras should be turned on and off. The two officers' body cams were not switched on and footage from the police auto failed to capture the incident .
Humanitarian organisation Palestinian Red Crescent told Ma'an, a Palestinian news agency, that at least 113 Palestinians had been injured in East Jerusalem and the West Bank.
Israeli police tightened security around Old City as Muslims protested against installation of metal detectors at a flashpoint shrine holy to both Jews and Muslims.
Thousands of believers refused to ascend the temple mount through the metal detector, spread out prayer mats in the streets and began to pray.
Israeli police said five officers were wounded.
Israel asserts there is no change to status quo and the metal detectors are necessary to stop further attacks.
Sacred to Muslims, Jews, and Christians, Jerusalem is home to the Al-Aqsa Mosque, which for Muslims represents the world's third-holiest site.
According to Israeli television Channel 2, Israeli police chose to remove metal detectors as of Saturday night and use handheld detectors instead.