The clandestine meeting came ahead of a G7 virtual summit in which leaders will likely seek more time to evacuate foreigners and Afghans from Kabul.
Within hours of his return, the Taliban announces that its rule would be "different" this time and an official says the Taliban will be accountable for its actions and will investigate reports of reprisals and atrocities.
Questions surround Khalilzad, an enigmatic diplomat who presided over US failures in Iraq and now the return of the Taliban to power in Afghanistan.
The state of Afghanistan today is the result of one strategic failure after the other, demonstrating the ineptitude of international interventions.
The current regional balance of power, in which Russia and China see the Taliban as the lesser of two evils, and a hasty US withdrawal helped the group march across Afghanistan, experts say.
Key politicians with background of anti-Taliban or anti-Soviet resistance are converging in their areas of influence to mobilise forces for a likely face-off with the marching Taliban. But rights groups fear such militias could become abusive force.
The Afghan Taliban said they are committed to peace talks as officials raised concerns over the stalling negotiations between the militants and government representatives in Qatar ahead of foreign troops' withdrawal in September.
A Taliban member familiar with, but not part of, the talks that resumed in Qatar says US envoy Zalmay Khalilzad met one-on-one with the Taliban's lead negotiator, Mullah Abdul Ghani Baradar.
Taliban is "really committed to peace, but think the obstacle for peace should be removed first," Taliban co-founder and political leader Mullah Abdul Ghani Baradar says in a rare televised appearance at the start of the two-day meeting in Moscow.
The longest peace talks between the US and the Taliban to end America's 17-year war in Afghanistan concluded on Tuesday night in Qatar, with both sides saying progress had been made, but no final agreement could be reached.
The talks are being seen as the most promising yet between the warring parties after Taliban co-founder Mullah Abdul Ghani Baradar joined for the first time, flying in from Pakistan.
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