Kerry, who held talks with Israeli Prime Minister Benjamin Netanyahu in Berlin on Thursday, met Abbas in Amman, where he was also due to meet Jordan's King Abdullah II, custodian of Jerusalem's Al-Aqsa mosque compound which has been the focal point of the unrest.
They both expressed guarded optimism going into the talks, which come a day after more than 80 people were wounded in clashes between Palestinians and Israeli troops in the occupied West Bank and Gaza Strip.
Abbas for his part said: "All the time we have the hope. We did not lose the hope."
The international community is seeking a halt to a wave of violence that many fear heralds a third Palestinian intifada, or uprising.
Kerry, his Russian counterpart Sergei Lavrov, EU foreign policy chief Federica Mogherini and UN Secretary General Ban Ki-moon -- members of the Middle East peacemaking Quartet -- called for "maximum restraint" after talks Friday in Vienna.
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