Over the weekend security forces surrounded the village of Burqin west of Jenin in the northern West Bank and arrested five Palestinians, including three brothers from the Jarrar family.
The demolition took place near the settlement of Maaleh Adumim, in the 60 percent of the West Bank known as Area C that remains under full Israeli control.
The young activist had become a symbol of resistance and muse for many Palestinians and humane supporters of the Palestinian cause, just like young Palestinian activist Ahed Tamimi, IsraaJabbis, who are now detained by Israeli police.
Israeli security Shin Bet and Border Police's counterterrorism unit known as Yamam said in a statement to journalists that Jarrar came out of a building in Yamoun village with an M-16 rifle and explosives and was shot immediately.
Israel had been hunting the final member of the cell.
Jarrar, 22, also personally participated in the attack, the Shin Bet said.
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Jarrar was seven years old when his father, the Hamas leader Nasr Jarrar, was killed by Israeli forces during the second Intifada in August 2002.
Israeli forces have dispersed to nearby towns in search of the attacker.
Monday's stabbing occurred near the major Israeli settlement of Ariel. The victim was identified by an internal settler communique as Itamar Ben Gal, in his 40s and a resident of Har Bracha settlement near the West Bank city of Nablus.
There has been a spike in Palestinian violence since President Donald Trump's December 6 recognition of Jerusalem as Israel's capital.
Most countries deem Israeli settlements in the West Bank, land Israel captured in a 1967 war that the Palestinians want for a future state, to be illegal.
At least 52 Israelis and five foreign nationals have been killed.