The Project on Government Oversight says it has been told by knowledgeable experts that the warhead nearly detonated in 2005 because an unsafe amount of pressure was applied while it was being disassembled, The Austin American-Statesman reports.
The U.S. Energy Department fined the plant's operators $110,000 last month.
An investigator for Project on Government Oversight says the weapon involved was a W-56 warhead with 100 times the destructive power of the atomic bomb dropped on Hiroshima.
The watchdog group says the problem was caused in part by technicians at the plant being required to work up to 72 hours each week.
They released an anonymous letter, reportedly sent by Pantex employees, warning that long hours and efforts to increase output were causing dangerous conditions at the plant.
A spokesperson for the Energy Department declined to respond to safety complaints in the letter.