Mr Netanyahu on Saturday denounced the assault as an "act of terrorism committed by a reprehensible person incited by wild hatred", and urged Palestinian President Mahmoud Abbas to condemn the attack, Xinhua news agency reported.
"The security forces are doing their utmost to maintain security and, to this end, will take all necessary measures," the Prime Minister said in a statement.
On Friday night, a 20-year-old Palestinian entered a family home in the settlement of Halamish, stabbing to death a father, his daughter and his son before he was shot and injured by a neighbor.
In a post on Facebook, the stabber said he was deeply concerned about the recent violence at the Al-Aqsa Mosque in annexed East Jerusalem and wanted to protect it.
The incident occurred amidst widespread Israeli-Palestinian clashes over the Al-Aqsa Mosque compound, East Jerusalem's most contested site. The site is known to Muslims as the Noble Sanctuary and the Jews as the Temple Mount.
The dispute started when Israel installed metal detectors at the entrance to the site on Sunday, following a shooting attack that killed three Israeli policemen last Friday. The detectors are seen by the Palestinians as a violation of the status quo at the Muslim-run compound and an attempt to gain more control over the site.
Anger reached a boiling point on Friday, when Israeli restricted access to the shrine to men under 50. Three Palestinians were killed in the clashes with Israeli security forces that ensued, and hundreds were injured.