Following Trump's speech, in which the USA president recognized Jerusalem as Israel's capital and ordered the State Department to begin preparations for moving the U.S. embassy to the city from Tel Aviv, Abbas slammed the move and said the United States has ended its historic role as the key sponsor for Israel-Palestinian peace talks.
Retaliatory Israeli airstrikes on the Gaza Strip killed two Hamas militants before dawn, as unrest simmered over US President Donald Trump's controversial declaration of Jerusalem as Israel's capital.
Mr Rajoub also signalled that the Palestinian leader would not meet with Mr Pence.
Pence is scheduled to arrive in the Palestinian territories on December 19 to meet Abbas as part of a tour of several countries in the region.
The White House warned on Thursday that cancelling the meeting planned for later this month in the West Bank would be "counterproductive", but Abbas has been under heavy domestic pressure to shun Pence following Trump's recognition of Jerusalem as Israel's capital.
"We express our appreciation to all United Nations Security Council members who have taken a position of courage and principle and have rejected and condemned the irresponsible decision of the US Administration to unilaterally and illegally recognize Jerusalem as the capital of Israel and move its embassy there".
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"The Arab League points out that members of the global community acknowledge Palestine's status as an occupied state", said AL's spokesman.
The Red Crescent said 12 Palestinians were injured by shrapnel from grenades or by blows from police. Meanwhile, protesters, the majority of them young boys and men, erected a barricade blocking the road and threw stones in the direction of an army base north of Bethlehem.
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.
"The US won't be a sponsor for peace again, and it's not qualified to do so", Al-Khalidi said, adding "there are many measures that will be taken by the Palestinian leadership soon".
The move was a break with the worldwide community, which has traditionally recognized Tel Aviv as the country's capital.
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.