President Trump said Wednesday that he didn't mention the U.S. service members who were injured in a Iranian strike against a U.S. base because they suffered "headaches." He initially said no Americans had been injured in the January 8 strike on Al Asad airbase in retaliation for the strike that killed Iranian Major General Qassem Soleimani.

CBS News' Weijia Jiang on Wednesday asked Mr. Trump, who was in Davos, Switzerland, for the World Economic Forum, to explain the discrepancy between the initial reports that there were no injuries and the Pentagon's statement on January 16 that several U.S. service members were injured.

"I heard that they had headaches and a couple of other things, but I would say that, and I can report, it is not very serious," said Mr. Trump.

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Jiang pressed Mr. Trump further, asking, "You don't consider a traumatic brain injury serious?"

"They told me about it numerous days later. You would have to ask the Department of Defense," Mr. Trump said. "No, I don't consider them very serious injuries, relative to other injuries that I've seen. I've seen what Iran has done with their roadside bombs to our troops, I've seen people with no legs and with no arms, I've seen people that were horribly, horribly injured, and that area, that war, in fact, [in] many cases, put those bombs, out there by Soleimani, who is no longer with us. I consider them to be really bad injuries. No, I do not consider that to be bad injuries, no."

United States Central Command spokesperson Captain Bill Urban said on January 16 that at least 11 U.S. service members "were treated for concussion symptoms from the blast and are still being assessed."

"As a standard procedure, all personnel in the vicinity of a blast are screened for traumatic brain injury, and if deemed appropriate are transported to a higher level of care," Urban said in a statement.

Major General Alexus Grynkewich, deputy commander for Operations and Intelligence, clarified Wednesday that the number of U.S. service members being treated for concussions is a bit higher, in the "teens." He also said that being evacuated doesn't necessarily mean a person has suffered a traumatic brain injury, but that he or she is reporting concussion symptoms.

Weijia Jiang and David Martin contributed reporting.