Mujahid said the Taliban representatives told Khalilzad that the presence of foreign forces in Afghanistan was a "big obstacle" to peace and that both sides "agreed to continue such meetings".
The Office of the President, ARG Palace, in a statement said Ambassador Khalilzad presented a report regarding his recent trips to the regional countries and emphasized that the United States is prepared for an all-out support to an Afghan-led peace process and efforts are underway in this regard.
A statement about Khalilzad's diplomatic tour released by the U.S. Embassy in Kabul did not confirm his meeting with the Taliban.
Last week the Taliban demanded a complete withdrawal of foreign forces as the only solution to end the war that began with the 2001 ousting of the former Taliban government by US -led forces after it refused to hand over Osama bin Laden following the 9/11 attacks on the United States.
Khalilzad returned to Kabul on Saturday after his first visit last Sunday where he met with a wide range of stakeholders. His 11-day trip includes stops in Afghanistan, Pakistan, the United Arab Emirates, Qatar and Saudi Arabia.
Terming the talks and Khalilzad's return to Kabul "as progress", Nazar Mohammad Mutmaen, an analyst familiar with Taliban leaders, said: "It is the first high-level meeting of U.S. officials with the Taliban and shows that both sides are giving peace a priority", he told Arab News. It added that the USA envoy reiterated Washington's support for "Afghan-led and Afghan-owned peace process".
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The Trump administration held their second direct talks with the Afghan Taliban in Qatar this week as the US State Department underlined the desire to push forward the Afghan peace process. It did not mention anything about the USA envoy's meeting with the Taliban.
The Taliban had reportedly met with USA officials in July after an unprecedented ceasefire in June which fueled hopes that negotiations could bring an end to fighting.
NYT noted that the White House ordered direct talks with the Taliban this summer to jump-start the peace process and Mr Khalilzad was "seeking to inject new energy into the long-stalled Afghan peace process".
"The Taliban have also suffered huge losses", Jawed added.
A US-led coalition forced the Taliban from power in 2001 in the aftermath of the 9/11 al-Qaeda attacks on Washington and NY.
The Taliban refuses to engage in direct talks with the Kabul government, dismissing it as "stooges of America".