"It will be ordinary Israelis and Palestinians who will have to live with the violence", Mladenov emphasized in calling upon political, religious, and community leaders to avoid using any rhetoric that could promote further escalation.
At the UN Security Council's emergency session on Friday to discuss President Trump's recognition of Jerusalem as Israel's capital, the US Ambassador to the United Nations Nikki Haley said the move advances prospects for peace, while the UN has only stifled resolution in the Israeli-Palestinian conflict.
The decision has sparked unrest within the Palestinian community, which views east Jerusalem as the future capital of an independent Palestinian state.
Abbas said that the U.S. had crossed a "red line" over the decision by President Donald Trump on Wednesday to move the USA embassy to Jerusalem from Tel Aviv, an aide said on Saturday.
Reuters reported that Egypt's Coptic Church has turned down a meeting request from the vice president due to Trump's decision.
Following the announcement by the U.S. president declaring Jerusalem the Israeli capital, Palestinians unleashed what they have called "day of rage" protests, resulting in two deaths and at least 1,100 injured so far.
Abbas recently met Jordan's King Abdullah II, after which they issued a joint statement noting that "any measure tampering with the legal and historical status of Jerusalem is invalid" and warning of the "dangerous" repercussions of the embassy move.
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Palestinian officials said Pence had been due to meet Abbas on December 19. He is set to travel to Israel and to the West Bank city of Bethlehem.
A Middle East Eye reporter on the scene witnessed two demonstrators being taken away by ambulances for treatment, and at least one instance of rubber-coated bullets being shot towards some protesters early in the morning.
However, Palestinian protests on Saturday were less intense than on the previous two days.
In East Jerusalem about 60 people demonstrated near the walled Old City, where paramilitary border police and officers on horseback tried to disperse the crowd with tear gas.
Israel had already responded on Friday to rocket fire with air strikes which the Gaza health ministry said wounded 14 people, including women and children.
"And President Abbas will not welcome him because of the statements he made" about Jerusalem.