Israel has rejected Palestinian calls for a protection force to be deployed in east Jerusalem to quell violence around the flashpoint Al-Aqsa mosque.
"Let me be crystal clear - Israel will not agree to any international presence on the Temple Mount. Such a presence would be a change in the status quo," Israeli Deputy Ambassador David Roet told the UN Security Council on Friday (local time).
The 15-member council met in an emergency session to discuss weeks of escalating violence between Israel and the Palestinians in Jerusalem and the territories.
On Friday, Palestinians torched a Jewish holy site in the West Bank as they staged a "Friday of revolution" against Israel and a man posing as a news photographer stabbed an Israeli soldier before he was shot dead.
UN Secretary-General Ban Ki-moon strongly condemned the "reprehensible" attack at Joseph's Tomb in the city of Nablus and called for those responsible to be brought to justice.
The two weeks of violence have also left 39 Palestinians dead, including alleged attackers, and hundreds more wounded in clashes with Israeli forces.
Gaza health ministry spokesman Ashraf al-Qudra told AFP that Yehya Abdul Qadir Farhat, 22, died on Friday "after he was shot directly in the head by the military in clashes close to the Beit Hanoun (Erez) crossing" in northern Gaza.
Mahmud Homaida, 22, was confirmed dead later in the day in clashes along the border.
Seven Israelis have been killed and dozens wounded.
The surge in violence has raised fears that a third Palestinian intifada, or uprising, might erupt.
Palestinian envoy Riyad Mansour urged the council to "urgently intervene to end this aggression against our defenceless Palestinian people" and called for "international protection".
Mansour said Israeli security forces must withdraw from "contact points" with the Palestinians, in particular in east Jerusalem.
There have been repeated clashes at east Jerusalem's Al-Aqsa mosque compound, the third-holiest site in Islam and the most sacred for Jews, who refer to it as the Temple Mount.
Muslims fear Israel will seek to change rules governing the site, which allow Jews to visit but not pray so as to avoid provoking tensions. Israeli Prime Minister Benjamin Netanyahu has said repeatedly he is committed to the status quo.
No draft resolution was presented to council members on Friday but French Ambassador Francois Delattre said he will circulate a draft statement appealing for calm.
In a bid to dispel fears, the council statement would also call for maintaining the status quo at the Al-Aqsa compound.
The council is to hold a ministerial-level debate on the Israeli-Palestinian crisis on Thursday to try to press for a de-escalation.
Meanwhile, Netanyahu expects to meet US Secretary of State John Kerry in Berlin next week, Israeli officials told AFP.
The US State Department was not immediately able to confirm that Kerry planned to meet the Israeli leader, but the news broke as he was already on a flight to Europe for planned meetings in Milan, Madrid and Paris.
Before leaving, Kerry had said he hoped to travel to the Middle East region "in the coming days" in order to try to cool tempers between Israelis and Palestinians amid a new spate of violence in Jerusalem.