The White House has warned against cancelling a planned meeting between Palestinian and US officials.
Amid indications that Abbas may withdraw from a planned meeting later this month, 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."
Pence 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 recognize Jerusalem as Israel's capital.
Jibril Rajoub, a senior member of Abbas's Fatah party, told AFP that Pence was "not welcome in Palestine" during his upcoming visit.
Rajoub also signaled that Abbas would not meet with Pence.
"And President Abbas will not welcome him because of the statements he made" about Jerusalem.
Abbas has not made similar comments and his office could not immediately be reached.
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.
Some Palestinian leaders have indicated that they no longer consider the United States an honest broker in the peace process.
Pence's trip now risks becoming a lightning rod for Palestinian anger.
In an effort to keep the trip on the rails, the White House is likely to only consider the meeting canceled if they hear that from Abbas himself.
Breaking off ties with Washington in such a public way would be risky, but the 82-year-old Palestinian leader could be under fierce domestic pressure to make the snub.