One may have been killed and the other taken hostage by the Taliban, according to an Afghan official.
A Nato statement said the two service members left their compound in Kabul on Friday but did not return.
The statement did not identify the pair by nationality but US officials said they are American.
The Afghan official said that a four-wheel drive armored vehicle was seen on Friday night by a guard working for the district chief’s office. The guard tried to flag down the vehicle, carrying a driver and a passenger, but it kept going, he said.
“They stopped in the main bazaar of Charkh district. The Taliban saw them in the bazaar,” he said.
“They didn’t touch them in the bazaar, but notified other Taliban that a four-wheel vehicle was coming their way.”
The second group of Taliban tried to stop the vehicle, but when it did not, insurgents opened fire and the two occupants in the vehicle shot back, he said.
Nato said a search is under way for the missing service members.
“Maybe they wanted to go to Paktia province or to the American base, but they came down the wrong road toward Charkh,” the Afghan official said. “They didn’t pay any attention to the police. Otherwise we could have kept them from going into an insecure area and now this unfortunate incident has happened.”
The only US service member known to be in Taliban captivity is Spc Bowe Bergdahl, of Idaho, who disappeared June 30, 2009, in Paktika province, eastern Afghanistan. He has since appeared on videos posted on Taliban websites confirming his captivity.