Article published on the 2008-07-23 Latest update 2008-07-24 09:40 TU
Palestinian chief negotiator Saeb Erakat said that he promised Abbas to be "a full and positive partner in the peace" and that he "will not lose a single moment in pursuing it".
On landing at Tel Aviv airport on Tuesday Obama stressed the importance of the US's ties to the Jewish state.
"The most important thing for me to share is the historic and special relationship between the United States and Israel, one that cannot be broken," he said.
Also on Tuesday, he said that hopes of peace were set back by the split between Palestinian President Mahmoud Abbas's Fatah movement and the Hamas movement, which controls Gaza.
Hours before his arrival, a Palestinian man was shot dead after launching a bulldozer into vehicles on a busy street and injuring at least 16 people near the King David Hotel where Obama is staying.
He condemned the attack, saying it was "a reminder of what Israelis have had to courageously live with on a daily basis for far too long".
Obama's declaration that Jerusalem should be the undivided capital of Israel has angered Palestinians.
Analyst Awad Duaibes told RFI's French service that Palestinians "have had bad experiences" after previous US elections.
"Every time there's a new American president, the first thing he does is put aside the Israeli-Palestinian conflict and the peace process," he sats.
"We've never seen a president who begins, two months after arriving at the White House, to say, 'I'm interested in resolving the Israeli-Palestinian conflict'. So that's very important, it would be a very big step from the American President if Barack Obama is elected."
Republican presidential hopeful John McCain has refused to visit the Occupied Territories.
Obama will travel to Germany on Thursday where he is set to make a key open-air speech in Berlin on US transatlantic relations.