A Palestinian passerby disputed the police account, saying he had seen police shout at the man, then shoot him four times. "I saw no knife on him," Hussam Wshah, 66, told Reuters.
Four Israelis and 24 Palestinians, including eight children, have died in 12 days of bloodshed, fueled by increasing Jewish visits to the al-Aqsa Mosque compound in Jerusalem (al-Quds).
Israel has poured reinforcements into Jerusalem, with no diplomatic initiatives on the horizon and Israeli leaders warning there could be no quick fix to largely "lone wolf" assaults.
Wshah, a Palestinian resident of East Jerusalem (East al-Quds), said he witnessed the fatal events on Monday from several meters away.
"The young man was walking when they shouted at him. He may not have heard them, and they fired directly at him four times and he fell to the ground," Wshah told Reuters.
Violence has spread from Jerusalem and the Israeli-occupied West Bank to Hamas-ruled Gaza.
Israeli Arabs have demonstrated in support of Palestinian protests in the occupied West Bank that have accompanied the surge in attacks.
Muslim anger has been stoked by increasing visits made over the past year by Jewish groups and right-wing lawmakers to al-Aqsa Mosque compound, which is also revered by Jews as the site of two destroyed biblical temples.
Israel has claimed it has no intention of allowing any change to the status quo at Islam's third holiest site, which Jews are allowed to visit but where non-Muslim prayer is banned.