According to Israeli police spokeswoman Luba Samri, the attacker approached the checkpoint, telling border police officers there that he felt unwell.
As he got closer, he pulled out a knife and stabbed one of the officers, who was slightly wounded. Another officer then fatally shot the attacker, Samri said.
The attack was the third stabbing since Saturday, when two Palestinians were shot, one fatally, after they attacked security forces in two separate incidents in the West Bank. A Palestinian assailant was also shot dead in another West Bank stabbing earlier this month.
Palestinians and Israelis are also watching the fate of a Palestinian prisoner who has been on a hunger strike in protest of his detention without charge.
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Israel's Supreme Court is hearing a petition today to free the prisoner, Mohammed Allan, on health grounds. On Friday, the 60th day of his hunger strike, Allan slipped into unconsciousness and is being treated in an Israeli hospital.
Israel recently passed a law that allows a judge to sanction the force-feeding or administration of medical treatment to prisoners on hunger strike, if there is a threat to the inmate's life.
But it's still unclear if the contentious procedure will be carried out in Allan's case.
Israel says the law is needed to deter Palestinian detainees from hunger strikes to pressure Israel for their release or other demands.
Israel fears the death of a prisoner on a hunger strike could trigger Palestinian unrest amid the stalled peace negotiations. Critics say force-feeding amounts to torture.