Saeb Erekat, a senior Palestinian peace negotiator, said Abbas planned to tell Obama that, if elected president, he must not waste time and must immediately turn his attention to the Israeli-Palestinian conflict.
Obama said on Tuesday in Jordan after a meeting with King Abdullah that he would work to bring Israel and the Palestinians together "starting from the minute I'm sworn into office".
But he has cautioned it is "unrealistic to expect that a US president alone can suddenly snap his fingers and bring about peace in this region".
Security was tight for Obama's West Bank visit, with helmeted riot police carrying truncheons and rifles lining the access road to the walled compound as he shook hands with an Abbas aide and then entered the building.
The Illinois senator's Middle East tour has been an attempt by the Democratic presidential candidate to bolster his foreign policy credentials ahead of the US's presidential election in November.
The visit is in contrast to John McCain, the Republican presidential candidate, who did not visit the West Bank during his time in the region.
Earlier on Wednesday, while meeting Shimon Peres at the Israeli president's official residence in Jerusalem, Obama pledged that that as president he would preserve the close ties between the US and Israel, and that Israel's security would be a top priority in his administration.
"I'm here on this trip to reaffirm the special relationship between Israel and the United States and my abiding commitment to Israel's security and my hope that I can serve as an effective partner, whether as a US senator or as president," Obama said.
At Israel's Yad Vashem Holocaust memorial, he laid a wreath, lit a memorial flame, and deemed the place to ultimately be "a place of hope".
He was also due to tour the Western Wall, Judaism's holiest site.
Obama's visit in the West Bank has generated some goodwill, particularly since his Republican rival, John McCain, did not visit the Palestinians during a Middle East trip earlier in the summer.
Nour Odeh, Al Jazeera's corrrespondent in Ramallah, said: "The Bush administration only began to be engaged in the Middle East peace process in November 2007 at Annapolis. That peace process is yet to yield any results and is not expected to conclude with a Palestinian state - as promised - at the end of 2008.
"There were a lot of Palestinian frustrations right before Barack Obama came to Ramallah ... but keep in mind that this visit to the West Bank town is only for 45 minutes. Obama is keeping the better part of his day visiting Israeli officials and concentrating on the very important Jewish vote in the US".
After visiting the West Bank, Obama will meet Tzipi Livni, the Israeli foreign minister, in Jerusalem, then fly by helicopter to the southern Israeli town of Sderot - the target of many Palestinian rocket attacks - and back to Jerusalem to meet Ehud Olmert, the prime minister.
He is then due to fly to Germany on Thursday for talks with Angela Merkel, the German chancellor.
Iran was also expected to figure high on the talks agenda, with many Israelis uncomfortable with Obama's openness to talking to Tehran.
Earlier on Wednesday, Obama met Ehud Barak, the Israeli defence minister, and the Likud bloc's Benjamin Netanyahu, who is the parliamentary opposition leader.
Barak's office issued a statement saying the two discussed "all the relevant issues" and the "future challenges facing Israel and the region" - such as Israeli-Palestinian peace efforts and Israel's determination that Iran not be allowed to build atomic bombs.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said: "Obama is a man whose foreign policy we don't know that much about so far, certainly as far as Middle East policy goes. This visit is designed to join up the dots, if you like.
"It will also tick the Israel box in terms of voters in the US, where there is a very broad consensus of support for Israel."