Flying in to Jordan from an interrupted visit to Rome, he first held talks with King Abdullah II as he pressed his bid to "continue to narrow the gaps" between the two sides, his spokeswoman said.
He then went into evening talks with Abbas who had just returned from the Arab League's annual summit in Kuwait, a US official said.
Under a July deal for the relaunch of the peace negotiations, Israel said it would release 104 Arabs held since before the 1993 Oslo peace accords in exchange for the Palestinians not pressing their statehood claims via the UN.
But there are growing fears Israeli Prime Minister Benjamin Netanyahu's cabinet may block the move.
"Israel is trying to worm its way out of releasing the prisoners. They will be held responsible for any repercussions of this," Palestinian minister of prisoners affairs Issa Qaraqe told Voice of Palestine radio.
He insisted Israel free all the prisoners.
If the releases do not go ahead as scheduled this weekend, Palestinian leaders are threatening to renew their diplomatic push at the United Nations.
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