Talks between Khalilzad and the Taliban have focused on USA and North Atlantic Treaty Organisation troop withdrawal and guarantees from the Taliban that Afghanistan would not again become a safe haven for terrorists to plan global attack like the airborne assaults on the United States in 2001.
"We've made clear to the Taliban that we're prepared to remove our forces, I want to be clear, we've not yet agreed on a timeline to do so", he said Tuesday.
Pompeo met with President Ashraf Ghani as well as General Scott Miller, who leads NATO's Afghanistan mission and the USA war effort in the country, as well as other high-level Afghan officials during the one-day visit to the Afghan capital.
Khalilzad accompanied Pompeo as he met with Afghan President Ashraf Ghani and his partner in power, Abdullah Abdullah, the country's chief executive.
About 20,000 foreign troops, majority American, are deployed in Afghanistan.
"All sides agree that finalizing a U.S. -Taliban understanding on terrorism and foreign troop presence will open the door to intra-Afghan dialogue and negotiation", Pompeo said.
More than 2,400 USA military personnel have been killed and more than 20,000 have been wounded since the beginning of the Afghan War in October 2001. The remainder are part of a bilateral counterterrorism operation against al-Qaida and Islamic State fighters.More news: Pompeo-Modi talks have 2 problems - Iran and trade
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He said the two sides are almost ready to conclude a draft text outlining the Taliban's commitment to join fellow Afghans in ensuring that Afghan soil never again becomes a safe haven for "terrorists".
The U.S. war in Afghanistan is now in its 18th year. Thousands of Afghan soldiers, police and Taliban were also killed. He added that discussions with the Taliban have also begun on USA troop withdrawal.
But momentum for talks with the Taliban is steadily building, with a special United States peace envoy for Afghanistan, Zalmay Khalilzad, pushing the process and insurgent leaders showing serious interest in negotiating for the first time.
Pompeo told reporters that the USA government was prepared to remove American troops from the country.
"The people of Pakistan and Afghanistan are bound by fraternal ties reinforced by historical, religious, linguistic and cultural affinities".
Political opponents of Ghani met Pompeo and USA officials.
It's not clear if the deaths were the result of the war, which at almost 18 years is America's longest running.