Afghanistan's security situation has worsened since North Atlantic Treaty Organisation formally ended combat operations in 2014, as the Taliban battle to re-impose Islamic laws following their overthrow in 2001 at the hands of US-led troops.
Senior Taliban officials met with a "high-ranking" USA delegation in Qatar on November 14, 15 and 16, the militant group said in a WhatsApp message, without mentioning Khalilzad.
"These were preliminary talks and no agreement was reached on any issue", he said in a statement on Monday. U.S. officials could not immediately be reached for comment as the State Department has refused to comment on reported talks with the Taliban.
The U.S embassy in Kabul declined to comment.
Earlier this month, the United States government's ombudsman for the American effort in Afghanistan issued a report that said the Taliban have strengthened their grip on the country over the past three years, with the Afghan government in Kabul controlling only about 56% of the country - down from 72% in 2015.
Khalilzad on Sunday said he was "cautiously optimistic", a peace settlement, which he preferred to call a "roadmap to Afghanistan's future", could be hammered out among rival Afghans.
"The second round of talks went on for three days".
The president said the younger generation represents the new Afghanistan; one that is willing to forget the past and look towards the future.
"The Taliban are saying that they don't believe that they can succeed militarily". In meetings in Kabul, Khalilzad is expected to press Afghan President Ashraf Ghani to cobble together his own negotiating team, which could prove hard given the deep divisions within the government.
He said that both political and military pressure is continuously being applied to push the Taliban to the negotiating table. When he visited Kabul in July, Secretary of State Mike Pompeo said the strategy "is indeed working".
Meanwhile, a top USA military officer said that the Taliban "are not losing" in Afghanistan, and much more needs to be done to bring peace to the war-torn country. "We used the term stalemate a year ago and, relatively speaking, it has not changed much", CNN quoted General Dunford, as saying.
The NATO-led Resolute Support mission involves 41 nations contributing more than 12,000 soldiers, equipment and training for Afghan forces. The Taliban have long refused USA demands to negotiate with the Western-backed government in Kabul, which the rebels view as a puppet regime.