The Israeli militant alleged that they were seeking to arrest the man after he allegedly shot at them in the occupied West Bank.
Israeli daily Haaretz said three officers were hurt in the shooting; two of them suffered serious wounds and one suffered a mild-to-moderate injury.
Police said Sunday that so far two gates leading to the holy site had been opened, equipped with metal detectors, adding that more than 200 people had entered.
According to the Border Police, during the attempt to arrest him Khalil drew a self-made weapon and aimed it at the Israeli forces, which then shot and killed him. "In response to the immediate threat forces fired towards the attacker resulting in his death", it said.
A Palestinian gunman who was killed by Israeli security forces in an overnight raid in the West Bank was a former member of the Palestinian security forces turned arms dealer, the Shin Bet said on Sunday.
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An additional Palestinian suspect was arrested in connection with Saturday's shooting terror attack near Ateret.
According to the army, the first incident took place when Amer opened fire on a vehicle of an Israeli colonist, near Ateret illegal settlement, and the second targeted a fortified military base, near Nabi Saleh.
According to the Shin Bet, Halil carried out the two attacks together with his fiancée, Rawan Ambar, because their families did not approve of their engagement.
"The ISA, Israel Police and IDF will continue to take determined action to thwart terrorist attacks and quickly solve those attacks committed against Israeli civilians and security forces", the Shin Bet stated.
Sources in Tirawi's village told AFP he had been detained by Palestinian security forces for a number of days in the past few weeks, and that he was wanted by Israeli security prior to the Saturday shootings.