He appealed to the Palestinian people and factions to "focus on the upcoming challenges facing the national project by taking advantage of the opportunity to achieve national unity".
"He asked to meet (Abbas) on the 19th of this month in Bethlehem, such a meeting will not take place", Jibril Rajoub said.
Trump's move to recognise Jerusalem as the capital of Israel sparked Palestinian protests, sporadic clashes and a call for a new intifada on Thursday as fears grew of fresh bloodshed in the region.
Pence is expected to visit Israel and the Palestinian territories sometime before Christmas.
Palestinian officials have said that prospects of both USA recognition of Jerusalem as Israel's capital and relocation of the American Embassy in Israel would spell the end of America's role as an interlocutor in the peace process between Israel and the Palestinians. According to Palestinian officials, the USA moving its embassy in Israel to Jerusalem or recognizing the city as Israel's capital is equivalent to siding with Israel's claim to all of Jerusalem.
Abbas said Trump has disqualified the United States from its traditional role as peace broker in the Middle East conflict.
He added that "the decision of the trump will not change the reality of al-Quds (the Arabic name for Jerusalem, which is claimed by Palestinians) - the Arab, Muslim and Christian city is the eternal capital of Palestine".
"Today, we finally acknowledge the obvious: that Jerusalem is Israel's capital", Trump said Wednesday.
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