Earlier this week, Trump said he does not consider potential traumatic brain injuries to be as serious as physical combat wounds, minimizing the severity of the injuries, saying he heard that some troops "had headaches, and a couple of other things, but I would say, and I can report, it's not very serious."
"And, we ask that he and the White House join with us in our efforts to educate Americans of the dangers TBI has on these heroes as they protect our great nation in these trying times. Our warriors require our full support more than ever in this challenging environment," Schmitz added.
Of the 34 service members, 17 of those who were injured have since returned to duty in Iraq.
Nine service members are still being treated in Germany. An additional eight service members who had been flown to Germany have since been sent to the United States for additional treatment.
Although traumatic brain injuries are not always immediately apparent, the disclosure of injured US service members suggested that the attack's impact was more serious than initial assessments indicated.
Mild traumatic brain injuries, commonly known as concussions, are a form of TBI. The most common form of TBIs in the military are mild TBIs, according to the Defense and Veterans Brain Injury Center.
This story has been updated to add more details about the Veterans of Foreign Wars.
CNN's Ryan Browne, Barbara Starr and Michael Callahan contributed to this report.