American officials separately confirmed that two US soldiers serving with Nato forces were missing, but did not comment on the Taliban claims.
In the eastern Afghanistan province of Logar, local radio broadcast offers of a $20,000 reward for information that led to the safe release of the pair.
"Early this morning two coalition personnel went missing," the announcement said. "They are believed to have been captured by insurgents somewhere in Logar province.
"They may have been separated from one another or maybe in the process of being moved to another location."
A Taliban spokesman said that three servicemen with the Nato-led International Security Assistance Force (ISAF) had been captured but one had died. He did not give further details.
The two unnamed US personnel were wearing standard military camouflage, according to the radio report.
One was described as about six foot tall and weighing 15st 10lbs with blond hair and brown eyes. The other was described as 13st 8lbs, bald with a thin moustache. 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.