Separately, a gun battle in the capital of Badghis province in the country's northwest left three police dead, provincial governor Abdul Ghafur Malikzai said.
Taliban insurgents stormed a commercial building housing a hotel in western Afghanistan, killing three security officials and injuring 10, officials said on Saturday, the latest in a surge of attacks despite reported progress in peace talks.
The NATO-led Resolute Support said it would not release the name of the soldier or give further details until 24 hours after giving notification of the death to the soldier's family.
In a telephone interview, Taliban spokesman Zabihullah Mujahed said the terrorist group was behind Saturday's killing, even as USA peace envoy Zalmay Khalilzad has been holding talks with the Taliban in recent weeks to try and negotiate an end to the war in Afghanistan. The US does not use tanks in Afghanistan. The discrepancy between the number of fatalities given by the US and the Taliban could not immediately be explained, but the Taliban often exaggerate their claims.
Members of Afghan delegations walk during the second day of Intra-Afghan conference for peace in Doha, Qatar July 8, 2019.
Two U.S. service member were killed on June 26 when attacked by the Taliban under small arms fire in Uruzgan Province, Afghanistan, the Pentagon said.
Women and children comprised half of those casualties (145 deaths and 83 injuries), according to the United Nations agency.
The U.S. top negotiator Zalmay Khalilzad described the recent discussions as "the most productive session to date".
A Taliban ambush in the same Afghan district late last month had killed two American soldiers.