After killing Sgt Hazan in a field near the village of Beit Amin, 42-year-old Amar threw the Israeli's body into a well.
Israeli Prime Minister Benjamin Netanyahu sent his condolences to the Hazan family and said the murder was further proof "that the fight against terrorism is constant".
Robert Serry, the UN Special Coordinator for the Middle East Peace Process called for calm following the "shocking" murder.
Avigdor Lieberman, chairman of the Knesset's Foreign Affairs and Defence Committee, claimed Amar's family were known to be affiliated to Fatah.
He said the attack showed that the Palestinian Authority had "no desire or intention" of making peace
