"This is a confidence-building measure," Mark Regev, a spokesman for Olmert, said.
He said Israel will release prisoners from the Fatah faction and other non-Islamist groups.
The names of those to be freed will now be drawn up by a special committee according to criteria which rule out the release of prisoners "with Jewish blood on their hands".
Israelis will also be able to lodge objections to any candidates identified for release.
|Israel has kept the Gaza border sealed amid renewed rocket fire [GALLO/Getty]
A senior Israeli official has said that none of the prisoners to be freed belongs to Hamas, the Palestinian faction in control of the Gaza Strip.
Israel has not said whether it would consider freeing Fatah inmates such as Marwan Barghouthi, the leader of the last Palestinian uprising, who is seen as a possible successor to Abbas.
In a similar move in August, Israel freed 198 Palestinian prisoners. More than 11,000 Palestinians are still held in Israeli prisons.
Such releases are highly emotive for Palestinians, who regard prisoners as symbols of resistance to Israeli occupation.
Eli Yishai, the trade and industry minister, from the ultra-Orthdox Shas party, voted against the release, calling the gesture "very dangerous, strange and dubious".
US-sponsored peace talks between Olmert and Abbas, rejected by Hamas, have shown little sign of progress.
Gaza border clashes
The offer to release prisoners comes as Israel also contemplates a major incursion into the Gaza Strip to combat Palestinian rocket attacks.
"Following mortar and rocket fire, the border crossings we had expected to open will remain closed," Shlomo Dror, the defence ministry spokesman, said on Sunday.
The Israeli military said on Saturday that its soldiers have battled Palestinian fighters along Israel's border with the Gaza Strip.
Clashes have continued at relatively low levels following an Israeli air raid and Palestinian rocket fire on November 4.
Israel and Hamas officials insist they are committed to maintaining the truce.
Hajj visa dispute
Meanwhile, Gaza-based Hamas authorities have threatened to prevent Muslim pilgrims from leaving the territory to attend the annual Hajj pilgrimage in Saudi Arabia, unless a dispute over visas is resolved.
Egypt has said it will only allow pilgrims to enter its territory from Gaza if their Saudi visa applications are submitted through the Palestinian Authority.
Hamas says it has submitted its own lists of pilgrims to the Saudi authorities for visa approval but Egypt has refused to recognise them.
Al Jazeera's Sherine Tadros said: "For another day those pilgrims tried to cross the Rafah border and were turned back again by the Hamas controlled security forces.
"Hamas has several reasons technical and legal for not allowing the pilgrims through ... of course we have a standoff here and there is mounting anger and frustration by these pilgrims who feel they are caught in the middle between this political struggle between Hamas and Fatah," she said.
For people in Gaza, the worsening humanitarian situation remains a great concern.
Israel has allowed food into the Gaza Strip for only three days since the flare-up of violence on November 4 prompted it to tighten its blockade of the aid-dependent territory.