It added that security forces had made arrests and seized weapons at Bruqin, also nearby, and at the Balata refugee camp.
The group which on Saturday said it carried out the attack is the armed wing of Palestinian president Mahmud Abbas's Fatah faction.
"We claim responsibility for the heroic operation in the colony of Ariel in which a Zionist officer was killed, in response to violations committed by the occupation government in Jerusalem," the group said.
Late Friday the Palestinian health ministry said a Palestinian in his 20s had been shot and killed during an Israeli army operation in the northern West Bank town of Azzun.
Forty-two people had earlier been hurt in clashes between Palestinians and Israeli police, according to the Palestinian Red Crescent, at the Al-Aqsa site venerated by Muslims and Jews in Jerusalem's old city.
The unrest occurred on the last Friday in the Muslim holy fasting month of Ramadan, and brought to nearly 300 the number of Palestinians hurt over a two-week period in clashes there.
Al-Aqsa mosque compound is in east Jerusalem, which Israel captured in the 1967 Six-Day War, along with the West Bank, and later annexed, in a move not recognised by most of the international community.
Israel has since built settlements in the West Bank that are considered illegal under international law but are home to around 475,000 Israelis.
The Al-Aqsa tensions came against a backdrop of wider violence since March 22 in Israel and the West Bank.
Thirteen Israelis, including an Arab-Israeli police officer, and two Ukrainians were killed in separate attacks inside Israel. Two of the deadly attacks were carried out in the Tel Aviv area by Palestinians.
A total of 27 Palestinians and three Israeli Arabs have died during the same period, among them perpetrators of attacks and those killed by Israeli security forces in West Bank operations.