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The sources said that the meeting was held at the United States Consulate General in Jerusalem, adding that Fayyad and Mitchell discussed the stalled peace process in the Middle East.
The sources declined to reveal in details what had been discussed between Fayyad and Mitchell, and only said the meeting was "positive."
Mitchell, who arrived in the region on Wednesday night, held talks on Thursday and Friday with Israeli leaders, mainly hawkish Israeli premier Benjamin Netanyahu and Palestinian President Mahmoud Abbas.
He had promised Abbas during their meeting in Ramallah on Friday that his Administration "wouldn't spare any effort to do all we can to help achieve the goal of the comprehensive peace in the Middle East."
However, Mitchell has so far failed to convince Israel to freeze or halt Israeli settlement, including the natural growth, where he and President Obama are pressing on resuming the peace talks between the two sides.
The Palestinian side insists that there will be no renewal of any peace negotiations with Israel, unless Israel expresses commitment to implement the U.S.-backed Roadmap plan for peace in the Middle East.
The plan calls on Israel to stop settlement activities in the West Bank for PNA security cooperation with Israel, and also calls for recognizing the vision of the two-state solution.