The Taliban have generally insisted on negotiating only with the United States, saying they will not enter talks unless U.S. troops leave the country. He began his official trip to the region a week ago that took him to Kabul, neighboring Pakistan, the United Arab Emirates, Saudi Arabia and Qatar. "Both sides agreed to continue meeting in the future", Taliban spokesman Zabiullah Mujahid said in a statement.
As Afghan security forces struggle to provide security, the USA has been seeking peace talks with the leaders of the Taliban insurgency.
FILE - Former U.S. ambassador to Afghanistan, now U.S. special envoy on Afghan peace, Zalmay Khalilzad speaks at the Mayflower Hotel, April 27, 2016, in Washington.
It was the second in the past four months amid reconciliation efforts 17 years after the U.S. invasion.
Taliban leaders will continue to meet for discussions with the newly appointed United States special envoy for peace efforts in Afghanistan, the Taliban said on Saturday, a move that could accelerate diplomatic engagement between the warring sides.
Khan added the Khalilzad's appointment showed the US now wants to find a political solution to the Afghan war since they failed to defeat the Taliban with force.
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But there are concerns over how they will manage as the Taliban and the Islamic State group step up attacks across the country.
Khalilzad was in the Afghan capital Saturday meeting with President Ashraf Ghani and Chief Executive Abdullah Abdullah, AP reported citing the embassy as its source.
The High Peace Council meanwhile said the authority welcomes efforts by the United States envoy for Afghanistan's peace process. "All citizens of Afghanistan must be a part of this reconciliation process", the statement quoted Khalilzad as saying.
But ongoing fighting has raised questions about the viability of the US strategy to end the war, which for the past year has focused on forcing the militants, largely with more air strikes, to the negotiating table.
Taliban spokesman Zabihullah Mujahid confirmed that Khalilzad met the Taliban leadership on Friday in Doha.
"Both sides spoke (about) an end to the occupation and a peaceful solution to the Afghan issue ..."
The Taliban have long demanded direct talks with Americans, instead of coming via Kabul but the Trump administration has assured the Afghan government that they will not be sidelined.