The Nato-led International Security Assistance Force (ISAF) had no official comment, but a Reuters correspondent in Logar heard local radio broadcast appeals offering a $20,000 reward for information leading to the safe release of the two.
“Early on Saturday morning two coalition personnel went missing. They are believed to have been captured by insurgents somewhere in Logar province,” the broadcast said.
“They may have been separated from one another or maybe in the process of being moved to another location.”
A Taliban spokesman told Reuters that three ISAF servicemen had been captured but one had died. He did not elaborate.
The two US personnel were last seen wearing standard US military camouflage, the radio broadcast said.
One was described as about six-foot tall weighing 100 kg with blond hair and brown eyes. The other was described as 86 kg, bald with a thin mustache. Both men have tattoos, the broadcast said.
“Coalition forces are offering $20,000 reward for any information that leads to the successful return of these two,” the statement said, without identifying the men.
There is believed to be only one other ISAF soldier being held by the Taliban, who released a video of him last Christmas.
Violence in Afghanistan has risen sharply since a reinforcement brought to 1,50,000 the number of foreign forces facing the Taliban and two other insurgent groups.