Twenty soldiers have accepted the offer so far, an Army spokesperson said.
Trump meet with military families and soldiers involved in the capture of Venezuelan President Nicolas Maduro.
One soldier was killed and another was injured Wednesday evening in what was called a helicopter training incident at Fort Campbell, the Army post said.
Fifty years after the fall of Saigon and the end of the Vietnam War, many U.S. combat veterans suffer from PTSD and other illnesses.
A swamp may have swallowed an Army vehicle, Lithuanian minister of defense says amid a search for 4 missing US soldiers.