Police confirmed the suspect's account was that he had left his home in the West Bank in the morning armed with a knife and headed towards Jerusalem.
Meanwhile, a Palestinian suspected of having killed a young Israeli woman has been arrested in a raid in the West Bank city of Ramallah, an Israeli police spokesman said.
Another 17 Palestinians were shot and wounded at different protest sites along the border, the ministry added.
14-year-old Hasan Shalabi who was killed by a bullet in the chest by Israeli sniper fire, was reported to be the grandson of the sister of Hamas leader Ismail Haniyeh, raising alarm over further potential escalation.
At least 248 Palestinians have been killed by Israeli fire since then, the majority shot during clashes, though others have been hit by tank fire or air strikes.More news: Racism and redemption: Virginia blackface row sparks national debate
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Gaza's Hamas rulers have organized mass demonstrations along the frontier every Friday since March, in part to protest against the Israeli and Egyptian blockade on the territory imposed when the Islamic militant group seized power in 2007. They have seen the death of about 190 Palestinians and an Israeli soldier.
IDF troops faced off against around 8,000 Palestinian rioters on the Israel-Gaza Strip border on Friday, as weekly Hamas-orchestrated unrest continued.
Palestinians have been holding protests every Friday since the end of last March, demanding the implementation of refugees' right of return to the lands they lost during the establishment of the state of Israel. Protests have dwindled in recent months after an informal agreement.
Amal A-Taramsi, a 44-year-old resident of Gaza City, was attending a mid-afternoon protest on the day in question, helping those "hurt by tear gas inhalation by spraying their faces with a saline solution", B'Tselem stated.