As part of a push to relieve Taliban pressure on the city in June, the Afghan military recaptured Khwaja Umari, a district about 10 miles from Ghazni, which had been under insurgent control for nine months.
"These six days have been the most productive of the rounds we've had with the Talibs", Khalilzad said in Qatar.
Khalilzad said that issue had been discussed with the Taliban but added that he could not comment further.
Talks between the USA and the Taliban are paused for two days as a group of Afghan politicians and civil society activists hold intra-Afghan dialogue at the same venue.
The Taliban has said it is "happy with the progress". We also send out a Weekly K+R Update, bundling together all the kidnap, ransom and extortion news of the week in one easy to read newsletter. "We have not faced any obstacles yet", he tweeted.
Officials have not confirmed any deaths among government intelligence employees.
Speaking anonymously because of the sensitivity of the talks, the US negotiator was responding to a timeframe Taliban officials told the AP months earlier. Addressing the opening session of the talks, German envoy to Afghanistan and Pakistan, Markus Potzel expressed gratitude to all the Afghan factions involved in the Intra-Afghan dialogue, which he said is in support of efforts to reduce the suffering of the Afghan people.
The Taleban, who have repeatedly refused to negotiate with the Western-backed government of Afghan President Ashraf Ghani, agreed to join the intra-Afghan summit on the condition that those there would attend in a personal capacity.
"President Ghani is quite comfortable with it", said Khalilzad.
Ghani s administration, which the Taliban consider a puppet regime, has also been excluded from the direct US-Taliban talks.
"It's up to the Afghans to decide when negotiations start", he said.
But Washington has made it clear the Taliban must talk with the Afghan government if they wish to seal a peace deal.
Khalilzad said the presidential poll could still go ahead as planned on September 28 even if no deal has been reached, but reiterated hopes a deal could be clinched in time.
Those issues include the withdrawal of foreign troops from Afghanistan, a permanent cease-fire, a Taliban guarantee that Afghanistan will not be used as a base for attacks in other countries, and an intra-Afghan dialogue that leads to a political settlement.
The Taliban and United States officials are trying to strike a deal on a Taliban demand for the withdrawal of USA and other foreign forces and a U.S. demand that the Taliban not let Afghanistan be used as a base for terrorism. "We want it and it is necessary for society, because media monitors the veins of society like a physician and then recommend them a solution, but freedom of the press should respect the faith and it should be used for the structure and construction of society not for destruction of individuals and society", he told TOLOnews.