It was unclear if the American was flying alone or with a member of the Afghan air force.
The Taliban on Wednesday accused the government of fabricating criminal cases against the prisoners.
Gen. Frank McKenzie said the U.S. did not increase force protection measures in Afghanistan as a result of the information.
As this story has evolved, there has been a subtle but important shift in the main actor.
A 21-year-old soldier from Texas was killed Friday in southwestern Afghanistan, Pentagon officials announced Saturday night.
So far the U.S. has reduced U.S. troop presence in Afghanistan from 12,000 to 8,600.
Russia's Foreign Ministry said Russia has only supplied weapons to the legitimate government of Afghanistan.
The Afghan government has insisted there was no military activity in the Taliban-controlled area at the time of the attack.
Pompeo and Mullah Abdul Ghani Baradar held a video conference in which Pompeo pressed the insurgents to reduce violence.
The Defense Department has been silent on the topic, referring questions to the White House.