One in five Palestinians have been imprisoned at some point by Israel.
Cabinet participants, speaking on condition of anonymity because the meeting was still going on, said the release was approved by a wide margin.
Olmert on Saturday had rejected a preliminary list of names to be released drawn up by the Shin Beth internal security agency and the justice ministry, as the sentences of several of the people on it were due to end soon anyway.
“The prime minister believed the release would not only not help Abbas, but would actually be seen as a slap in the face,” a senior government official told AFP on condition of anonymity.
Olmert has ordered a new list drawn up, with prisoners on it having at least a third of their sentence left to serve.
They are all to be members of secular Fatah and “men who can reinforce the moderates among the Palestinians,” Miri Eisin, Israeli government spokeswoman, said.
Israel currently holds more than 11,000 Palestinian prisoners, just over half of them having been convicted of an offence and more than 800 of them being held without charge.