Mr Khan, now Afghanistan's power-and-water minister, was deposed in 2004, partly due to an offensive by militants in Shindand district, around Azizabad.
Mr White, who was hired to help guard Shindand airbase in the western Afghan province of Herat, was killed in 2007 by a rival Afghan security contractor.
But the coalition said the airstrike was called in by Afghan and coalition troops as they embarked on a raid to arrest a Taliban commander in Shindand.
The head of the official veterans' committee, Ruslan Aushev, said Sheikh Abdullah - real name Bakhretdin Khakimov - was tracked down in Shindand district after a year-long search.