The return to direct contacts between the sides gave US Secretary of State John Kerry his first concrete achievement after months of shuttle diplomacy yesterday.
The US said preliminary talks would begin today, but it remains unclear whether they will lead to a formal resumption of peace talks that broke down in 2008.
Despite a return to the table, neither side appeared upbeat. Each has blamed the other for the lack of success in 20 years of negotiations interrupted by bouts of violence.
The State Department said Kerry called Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas after the Cabinet vote and invited them to send teams to Washington.
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State Department spokeswoman Jan Psaki said the teams would meet today and tomorrow to "develop a procedural plan for how the parties can proceed with the negotiations in the coming months."
Talks on a final peace deal are to last six to nine months.
Netanyahu, seeking to overcome stiff opposition from ultra-nationalists, told his Cabinet that "resuming the political process at this time is important for Israel," noting that any deal would be submitted to a national referendum.
Erekat welcomed the vote on the prisoners as a "step toward peace," one he said is long overdue.
Negotiators made progress in previous rounds, and the outlines of a deal have emerged a Palestinian state in most of the West Bank, Gaza and east Jerusalem, lands captured by Israel in 1967, with border adjustments to enable Israel to annex land with a majority of nearly 600,000 settlers.