Golsteyn told Fox News in 2016 he killed the suspected bomb maker.
"There's limits on how long you can hold guys," he said at the time. "You realize quickly that you make things worse. It is an inevitable outcome that people who are cooperating with coalition forces, when identified, will suffer some terrible torture or be killed."
That interview led the investigation to be reopened after a series of on-and-off investigations, Fox News reported. It had previously been dropped in 2014.
The Washington Post reported that Trump's tweeted statement could impact Golsteyn's military prosecution. It is expected that the commander chief does not make statements that would influence an open case.