(CNN) A congressional candidate who lost his eye while serving in Afghanistan said on Monday that a joke made on "Saturday Night Live" about his appearance was "dark" and that the show should have rethought the joke, but added that he doesn't want a "hollow" apology.
"The first part of that skit was just strange ... The second part, I think, is when it just became dark," Republican Dan Crenshaw, who is running for Congress in Texas' 2nd district, told CNN's Alisyn Camerota on "New Day."
"We have thick skin, but as veterans, it's hard for us to understand why war wounds would elicit such raucous laughter from an audience," he said, adding, "I think they should've rethought that joke a little bit -- if you can even call it a joke."
The joke, made by comedian Pete Davidson, came during an "SNL" segment in which Davidson gave his "First Impressions" of the appearances of several candidates.
"This guy is kinda cool, Dan Crenshaw," Davidson said on this weekend's show, next to a photo of Crenshaw. "You may be surprised to hear he's a congressional candidate from Texas, and not a hit man in a porno movie."
"I'm sorry, I know he lost his eye in war, or whatever," he added.
Crenshaw, a Navy SEAL who did five tours of duty, lost his right eye when he was hit by an IED blast in Helmand province in 2012 during his third deployment, according to his campaign website. Surgeries restored sight in his left eye. He recovered and ultimately deployed twice more.
Crenshaw was medically retired in 2016 with two Bronze Stars, the Purple Heart and the Navy Commendation Medal with Valor, according to his biography.
On Monday, he told Camerota that he isn't going to demand an apology from Davidson, whose father was a firefighter who died responding to the 9/11 attacks.
"I do not demand an apology. He probably should apologize," Crenshaw said, adding, "I don't want some hollow apology."
"I think he's exposed himself. I think he's exposed himself for who he really is," he said of Davidson. "I wish him well."
On Sunday, Crenshaw, who faces Democrat Todd Litton on Tuesday, reacted to the joke in a tweet, writing that, "I hope @nbcsnl recognizes that vets don't deserve to see their wounds used as punchlines for bad jokes."
Crenshaw did provide a suggestion to Davidson and his SNL coworkers for how to help veterans.
"I think what him and maybe the producers at SNL should do is pool their money together, let's throw a figure out there -- a million dollars -- and we will donate that to a series of veterans non-profits that helps veterans," Crenshaw said, listing off several organizations.
"There's a lot of veterans that really need help, and frankly, this kind of thing is offensive to them," he told Camerota. "They feel laughed at."
Crenshaw also told Camerota that he supports President Donald Trump's deployment of thousands of troops to the southern border to prevent the entry of a large of group of Central American migrants headed for it.
"We need to stop thousands of people from illegally crossing from one side of our border to the other," he said.
"If you simply allow that to happen or we pretend that there's just nothing to see down there, then we're setting a precedent. We're setting a dangerous precedent where there are no laws enforced in our country."
When Camerota told Crenshaw that the migrants' entry to the US won't be chaotic because of the processes that are used to admit people, he expressed skepticism.
"Well, how do you know?" he asked Camerota.
"Well because there were other so-called caravans in previous years that have shown up at the border and we treated them like asylum seekers ... it wasn't a crisis by the time it showed up at our border," she replied.
"And maybe it won't be this time, either," Crenshaw said. "But to not be prepared for it, I think, would be a disservice to the American people."