The two sides will meet despite Israeli anger at the killing of an off-duty Israeli senior police official in the occupied West Bank on Monday on the eve of the Passover Jewish holiday. The policeman's wife and a child were wounded.
"They're going to be meeting again tomorrow," State Department spokeswoman Jen Psaki said. "The parties are working on determining if there's a path to extend the negotiations for a period of months past April 29th."
Asked about the killing, Psaki urged both sides "to exercise restraint and avoid any actions that would raise tensions."
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The peace talks appeared on the verge of collapse this month when Israel refused to carry out a promised prisoner release after the Palestinians signed on to 15 international conventions, in contravention of the agreed-upon principles which Kerry negotiated as a pre-condition to resuming peace talks.
Israel called off the prisoner release unless it received assurances the Palestinian leadership would continue the talks past the deadline.
In response, the Palestinians signed the treaties, including the Geneva Conventions on the conduct of war and occupations, a defiant assertion of statehood that surprised the United States.
US Secretary of State John Kerry, who revived the peace talks in July after a nearly three-year hiatus, has sought to place the onus on the two sides for continuing the negotiations.
The main issues in the more than six-decade conflict include borders, security, the fate of Palestinian refugees and the future of Jerusalem, which both sides claim as their capital.