Abdul Latif Rustayee, the director of a hospital in Qala-e-Naw, said the 10 wounded, including four security force members, were rushed to hospital.
Meanwhile, the Ministry of Interior spokesman Nasrat Rahimi said a group of 3 suicide bombers launched the attack on a hotel in the city at around noon time.
At least four Afghan security forces and a U.S. service member have been killed in two separate attacks claimed by the Taliban as violence continues across Afghanistan despite efforts to end the 18-year war.
Officials said two of the gunmen were killed and one suspect had yet to be apprehended.
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.
The service members death brings to 10 the number of United States troops killed in Afghanistan so far this year, compared to 12 in 2018.
American officials have expressed a desire to reach a peace deal by September 1, ahead of Afghan presidential elections scheduled for later that month.
It's unclear whether the death was related to a roadside bombing that the Taliban claimed Saturday, saying it had "blown apart" an armored USA vehicle in an area of Wardak province along the Kandahar-Kabul Highway, about 50 miles south of the Afghan capital and some 25 miles west of a coalition base known as Camp Dahlke in Logar province.
USA military statement announcing the killings of the US service members was a terse, two-paragraph announcement.
Secretary of State Mike Pompeo, left, walks from a helicopter with U.S. Ambassador to Afghanistan John Bass in Kabul, Afghanistan on June 25, 2019.
The U.S. top negotiator Zalmay Khalilzad described the recent discussions as "the most productive session to date".