Violence erupted for a third day in Gaza in response to President Donald Trump's announcement on Wednesday, which overturned decades of USA policy towards the Middle East.
The vice president is due to travel to Egypt and Israel in the second half of December, a visit that has taken on extra significance in the wake of president Donald Trump's decision to recognise Jerusalem as Israel's capital.
On Wednesday, Jordan and Palestine requested an emergency meeting between Arab foreign ministers to discuss future actions in response to the United State's decision to declare occupied Jerusalem as Israel's capital.
Abbas said that the United States had crossed a "red line" over the decision by President Donald Trump on Wednesday to move the U.S. embassy to Jerusalem from Tel Aviv, an aide said on Saturday.
Separately, Egypt's Coptic Church has announced that its head had canceled a meeting with Pence in Cairo in protest against Washington's decision on Jerusalem.
Israeli air strikes killed two Palestinian gunmen on Saturday after militants fired rockets from the enclave into Israel on Friday, which had been declared a "day of rage" by Palestinian factions.
Abbas did not personally comment on the issue.
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Police said they arrested two young men from the Israeli Arab town of Arara. Shops were shuttered in Jerusalem's Old City.
Abbas's Fatah organisation urged Palestinians to "keep up confrontation and broaden it to all points where the Israeli army is present" in the West Bank.
Meanwhile, the Marxist-Leninist Popular Front for the Liberation of Palestine (PFLP) cancelled its 50th anniversary commemorations to protest against the Jerusalem embassy move on Saturday.
In Gaza, mourners vented their anger at the funerals of two people killed during clashes at the border fence on Friday and the two Hamas militants killed early on Saturday. About 60 Palestinian youths threw stones at Israeli soldiers across the Gaza-Israel border and the health ministry said at least 10 were wounded by Israeli fire.
Across the Arab and Muslim worlds, thousands more protesters had gathered to express solidarity.
Responding to rumors the meeting could be called off, a White House aide said Pence "still plans to meet with Abbas as scheduled" and "believes it would be counterproductive for him to pull out of the meeting".