Abbas and Olmert, who was forced from office three years ago, had spent months negotiating a potential peace deal. Abbas said Olmert had told him he would release several hundred prisoners as a goodwill gesture in advance of peace talks, but then said prisoners' release would have to await conclusion of a deal on the release of Israeli soldier Gilad Shalit.
Abbas said Olmert told him, "I promise you when we conclude Shalit and everything is OK, I will give you, not the same number, not the same quality, more."
Time said press reports at the time mentioned 2,000 prisoners.
Abbas said Olmert "asked me, please keep it secret, confidential between us, because we don't want to affect the deal with Shalit."
Negotiations for Shalit's release between Abbas and Olmert fell through but Abbas said Netanyahu should keep his predecessor's promise.
"Now the deal is over, and we will ask them to fulfill their promises," Abbas said.
Abbas said he told U.S. diplomat Daniel Rubinstein of the deal during a meeting in Ramallah Wednesday.
Neither Rubinstein nor Olmert could be reached Wednesday night, the beginning of the Jewish holiday Hoshana Rabbah.
Shalit was released Tuesday to Israel, and Israel has released the first 477 of 1,027 Palestinian and Israeli Arab prisoners it agreed to free in exchange for Shalit's release.