Tuesday's request came a day after Israel said it was suspending operations of an observer force in the city of Hebron (al-Khalil), after 20 years.
Palestinian official Saeb Erekat said the UN should "guarantee the safety and protection of the people of Palestine" until "the end of Israel's belligerent occupation”, AP reported.
Israeli Prime Minister Benjamin Netanyahu's office said it would not extend the mandate of the Temporary International Presence in Hebron (TIPH), saying "we will not allow the continuation of an international force that acts against us."
TIPH has deployed unarmed civilian observers since 1997. Hundreds of hard-line Israeli settlers guarded by soldiers live in the heart of Hebron, which has over 200,000 Palestinians.