Earlier he met with Israeli Prime Minister Benjamin Netanyahu for the third time on his extended trip.
Mr Mitchell is engaged in fresh attempts to get a deal on Jewish settlement activity.
He is hoping for an agreement before all sides meet at the UN General Assembly in New York next week.
Israeli media reports say that Mr Mitchell will hold further talks with Mr Netanyahu before the Jewish New Year holiday begins on Friday evening.
On Thursday, Mr Netanyahu urged world leaders to reject a UN report on the war in Gaza earlier this year.
The report concluded that Israel deliberately used "disproportionate force" in its three-week operation in Gaza in December and January.
It said both the Israeli army and Palestinian militants committed war crimes, and possibly crimes against humanity.
'Construction will continue'
Mr Mitchell has prolonged his trip to the Middle East for several days as he works for a deal on freezing Israeli settlement activity in the occupied West Bank.
Palestinian Prime Minister Salam Fayyad demands settlement freeze
The US is seeking a moratorium on settlement building that would be acceptable to the Palestinian side.
Mr Abbas and the US administration have been demanding a complete freeze on Israeli construction activity.
Mr Netanyahu has offered a temporary freeze for several months, but not in East Jerusalem or in cases where homes have already been approved.
On Thursday he gave no indication there would be a freeze in the West Bank.
"There is a slowdown in settlement construction, but not a freeze," he said. "There are 2,400 units being built, and their construction will continue."
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