Zalmay Khalilzad, an Afghan-born former U.S. ambassador to Kabul, has been leading Washington's efforts to encourage negotiations between the Taliban and the Afghan government to end the 17-year-old war.
A statement from the U.S. embassy in Kabul said Khalilzad would meet President Ashraf Ghani and Chief Executive Abdullah Abdullah.
U.S. officials have been tight-lipped about the meetings in Abu Dhabi, attended by officials from Saudi Arabia, the United Arab Emirates and Pakistan.
But a Taliban statement said the two days of talks concentrated on the withdrawal of foreign troops, a central demand of the movement, as well as the treatment of Taliban prisoners and civilian casualties from air strikes.
Washington insists that any peace settlement must be agreed between the warring Afghan sides but the Taliban have so far refused to talk directly with the Afghan government, which they consider an illegitimate foreign-appointed regime.
U.S. officials have been trying to persuade countries including Pakistan and Saudi Arabia to press the Taliban to agree to direct talks. Khalilzad met Pakistan's army chief on Wednesday ahead of his visit to Kabul. (Reporting by James Mackenzie; editing by Andrew Roche)
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