Israel's release of the prisoners on Friday is seen as a move to increase support for Abbas' interim government, in his power struggle with Hamas.
A festival of several thousands chanting, clapping Palestinians greeted the prisoners as their buses rolled into Abbas' headquarters in the West Bank city of Ramallah.
Prisoners were hoisted onto the shoulders of dancing supporters, before they performed noon prayers in a large, open-sided tent.
"This is the beginning," Abbas said, wearing a black-and-white checkered baseball cap, a symbol of Palestinian nationalism, against the fierce sun.
"Efforts must continue. Our work must continue until every prisoner returns to his home."
Israeli officials said 85 per cent of the prisoners being released were from the president's Fatah faction.
The others are from smaller groups such as the Popular Front for the Liberation of Palestine [PFLP].
None of those released are connected to Hamas.
The prisoners, bound and handcuffed, left Israeli prisons early on Friday, aboard buses that took them to the West Bank.
All the inmates were required to sign an undertaking not to engage in anti-Israel violence.
At an Israeli military checkpoint in the West Bank, the prisoners got off the buses, some kissing the ground, and boarded Palestinian buses that took them to Ramallah, to be reunited with their families.
"All the suffering, all the pain is gone," Iyad Milhem, one of the released prisoners, said. "But we still hope for the release of all the other prisoners."
Prominent among those release released was Abdel Rahim Malouh, second-in-command of the PFLP, which carried out the assassination of Rehavam Zeevi, an Israeli cabinet minister, in 2001.
Malouh, 61, was arrested in 2003 and is said to be ill.
A member of the Palestine Liberation Organisation's executive committee, he is considered close to Abbas and could serve as a mediator with Hamas.
At the celebrations in Ramallah, Malouh said: "This is a day of joy for our people and this joy will only be complete with the release of all our prisoners."
Güncelleme Tarihi: 22 Temmuz 2007, 00:22
The Palestinian prisoners were also to pay homage at the grave of Abbas's late predecessor, Yassir Arafat.
Israel had agreed to release 256 prisoners, but Eli Gadizon, of the Israel Prisons' Service, said one was held back for further security checks.
None of the prisoners being freed on Friday were directly involved in attacks on Israelis, according to Israeli officials.