He quoted Abbas as saying at a meeting of his Fatah party on Friday that: "I met Shimon Peres four times in Amman and London in an attempt to restart negotiations and the peace process on a correct foundation."
The official, speaking on condition of anonymity, added that Israel's Prime Minister Benjamin Netanyahu had thwarted those efforts.
"Shimon Peres assured me that the negotiations between us could lead to results that could be adopted by the Netanyahu government," the official quoted Abbas as saying.
"After the first four meetings, a fifth was scheduled in Amman, but Shimon Peres apologized and said, 'I'm sorry but the government does not accept that we negotiate and I cannot do anything,'" Abbas said at the Friday gathering, according to the official.
Israeli media reported in early August the cancellation of a planned secret meeting in Amman between Abbas and Peres after Netanyahu's refusal to give the president a clear mandate for negotiations.
A spokesman for the Israeli president, whose post is largely symbolic and ceremonial, declined comment.
In the absence of negotiations, the Palestinians are to present their bid for United Nations membership on September 20, Palestinian Authority Foreign Minister Riad Al-Malki said Saturday, a move firmly opposed by Israel.