Haag, 35, said Axel "saved my life."
Haag now tours the country explaining how service dogs help wounded veterans. Sunday's dispute with American Airlines occurred on Haag and Axel's way home from California, where Axel was named the winner in the Service Dog category at the 2015 American Humane Association Hero Dog Awards Saturday night, the American Humane Association said.
Haag said he, his wife and Axel made it through security in Los Angeles just fine Sunday. But later, a gate agent pointed to Haag and told him to come to the desk, he said.
"The first thing this guy asked me is, 'Is that a real service dog?'" Haag said. "I just find that question kind of odd because nobody at the airport has asked me that and I fly all the time. I said, 'Yes.'"
Haag said the agent then asked him to identify his disability, which Haag said, "Is the question that you're not allowed to ask ... The next thing out of his mouth is 'Where is your paperwork.' That's another thing they can't ask.
"The next thing they ask me is, ‘What does the dog do for you?' I tell him the dog does a bunch of stuff for me. He didn't really like that answer," Haag said. "I tried to start telling him the tasks; he starts to tell me that I'm noncompliant and my dog can't fly because I can't produce any paperwork.
“He didn't let me answer my questions. At that point I started to produce my ID that I have. He picks up the ID and says it's fake.”
"I then tell him I called eight days ago, registered him with your disabilities department. I flew out here three days prior on the same airline and I didn't have any issues," Haag said.
Haag said his wife was crying during the ordeal, which was in front of about 200 people at the American Airlines desk. He said a manager for the airlines told them to go home and come back with paperwork, so Haag and his wife spent another night in Los Angeles and took another flight Monday.
American Airlines spokesman Victoria Lupica confirmed to ABC News today that Haag, his wife and Axel did travel with American Airlines and ultimately reached their final destination in Virginia.
American Airlines said in a statement, "We are happy to say that Capt. Haag, Axel and his wife traveled with us earlier yesterday. We have apologized to both Capt. Haag and his family for the confusion with Sunday’s travel plans."
According to the American Humane Association, "Axel was denied entry on the American Airlines flight despite following the air carrier’s own requirements, which state that to show that an animal is a service animal, you must provide at least one of the following:
Animal ID card; Harness or tags; Written documentation to verify the service; psychiatric or emotional support status of your animal; Credible verbal assurance.
Axel had a harness and vest clearly identifying him as a service dog, and the airline was given credible verbal assurance at the time a boarding pass was issued. At the time of boarding, however, an American Airlines representative began to ask additional questions, including questions about his disability and demanding additional documentation. An airline representative later stated to American Humane Association’s legal counsel that Capt. Haag needed to have a medical alert card, which is not, in fact, a requirement."