Another stabbing occurred today in a separate West Bank settlement, wounding a 30-year-old woman.
The Palestinian assailant was shot by security personnel and taken to hospital after the attack in Tekoa south of Jerusalem, with conflicting reports on his condition.
While yesterday's killing was part of a months-long wave of violence, it was the first inside a Jewish settlement home, provoking fears that the attacks were worsening and that Israel would impose a harsh security crackdown on Palestinians.
"Whoever tries to harm us, we will bring him to justice," Netanyahu said. "In the end he will be found and he will pay the full price."
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Israel's military confirmed it was searching for the suspect but declined to provide further details. It also said Palestinians who work in settlements in the Hebron area were not allowed in today.
The woman killed was identified as Dafna Meir, a 38-year-old nurse and mother of six. At least some of her children, aged four to 17, were home at the time, but were not hurt.
Her death brought the toll in the recent violence to 24 Israelis and 155 Palestinians killed since October 1.
Many of the Palestinians killed have been attackers, while others have been shot dead by Israeli forces during protests and clashes.
Israel's government has come under heavy pressure over the spate of attacks, and yesterday's killing was likely to further raise tensions.
Some analysts say the attacks have been in part driven by frustration with the complete lack of progress in peace efforts, Israel's occupation of the West Bank and the fractured Palestinian leadership.