Al Jazeera's Nour Odeh, reporting from Ramallah, said that Palestinians celebrated by dancing and playing music as they waited for the convoy of buses carrying the prisoners to arrive for a reception at Abbas's presidential compound.
"The Palestinians have long argued that Israeli jails must be emptied of Palestinian political prisoners, as they are seen here," she said.
"This a central issue for Palestinian politics, one that is regarded as one of the most important, that can mobilise public opinion.
"This is one thing that the Palestinian president can boast about, even though the Palestinian Authority has maintained that the identity, the political affilitiation and the time served of the prisoners being released today has been the sole decision of Israel," Odeh said.
| About 11,000 Palestinians will remain in Israeli prisons after Monday's mass release [Reuters]
Two of the longest-serving Palestinian prisoners in Israeli jails, for whom Israel has made a rare exception to its policy of not freeing those implicated in deadly attacks on its citizens, were among the 198 detainees freed.
Said al-Attaba, 56, has been serving a life sentence since 1977 for killing an Israeli woman, and Mohammed Ibrahim Abu Ali, 51, known as "Abu Ali Yatta", who has been behind bars since 1979 for killing an Israeli reservist.
"This is a day of joy for the fighters of freedom and independence," al-Attaba said after his release.
"It is like a wedding celebration for the Palestinian people, but our joy will not be complete until all Palestinian prisoners are released."
Israel had earlier said it would release 199 prisoners, but one of those on the approved list remains in detention because of pending criminal charges.
Mark Regev, an Israeli government spokesman, said on Monday: "It is a gesture towards the Palestinian leadership to strengthen moderate and pragmatic forces."
"We hope it will contribute to a positive climate. It is not easy to release prisoners, and particularly those who have been involved in murderous terrorist attacks."
Ghazi Hamad, a Hamas official in Gaza, told Al Jazeera that he welcomed the prisoner release but criticised Israel was using it as a political tool by only releasing Fatah supporters from the West Bank.
"We know that sometimes they try to increase the divisions between the Palestinians, increase the gap between Gaza and the West Bank, to create troubles and more troubles," he said.
"We as Palestinians want all the prisoners to be released, from Gaza and the West Bank."
Ehud Olmert, Israel's prime minister, proposed the release earlier this month, hoping to support Abbas, whom he has met on a roughly fortnightly basis since peace talks were formally relaunched in November.
However, the two sides have made little tangible progress in resolving key issues, such as border, the status of Jerusalem and the right of return for refugees.
Rice is visiting the region in an attempt to give the process a kick start.