Since the start of October, at least 15 Israelis have been killed in stabbing and gun attacks on civilians, while more than 80 Palestinians have died, many of them attackers.
Four more Israelis were stabbed and wounded in the southern city of Kiryat Gat today, and an American was among five civilians killed on Thursday in Palestinian attacks.
The United States has called for both sides to take "concrete steps" to reduce tension, end provocative rhetoric and ensure access to Jerusalem holy sites.
But they admitted they were not expecting to strike any new agreement on a return to peace talks and would simply try to walk the parties back from the immediate conflict.
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Until two years ago the United States was the leading mediator in peace negotiations designed to leave Israel and Palestinian living side-by-side as two independent states.
That process collapsed. US officials stressed that they have no plans to revive it, and are simply trying to cool tempers and tamp down the current outbreak of violence.
"We're trying to encourage both of them to do the kind of things we think will be helpful and in their interests.
Kerry met Netanyahu in Washington earlier this month and urged him to "improve conditions for the Palestinians and try to get things moving in a more positive direction."
"Nothing concrete has come out of that yet," the US official admitted, adding only that a "variety of ideas were talked about" without getting into specifics.
The situation with the Palestinian leadership is even less promising, and Kerry's talks with Abbas will focus on how "to prevent the Palestinian authority from collapsing."
"The secretary has talked about incitement before and we'll obviously stress that," the official said, in an anonymous briefing to reporters before the trip.
Last month, Kerry met Jordan's King Hussein in Amman and endorsed a plan to install security cameras around the Al-Aqsa mosque on Jerusalem's Haram al-Sharif Temple Mount.