Mr. Buttigieg has often invoked his military service. His first Iowa television advertisement began with him saying, “as a veteran.” During an exchange about gun violence in the October Democratic debate, Mr. Buttigieg told former Representative Beto O’Rourke of Texas, “I don’t need lessons from you on courage, political or personal.” And in December, he responded to a debate barb from Senator Amy Klobuchar of Minnesota, who said that his devotion to the First Amendment was a “talking point,” by suggesting his time in the military was sufficient evidence of his devotion to the Constitution.

“Let me tell you about my relationship to the First Amendment,” Mr. Buttigieg responded then. “It is part of the Constitution that I raised my right hand and swore to defend with my life. That is my experience. And it may not be the same as yours, but it counts, Senator. It counts.”

Ms. Klobuchar, who had not brought up Mr. Buttigieg’s military service, was immediately put on the defensive and sought to shift the discussion away from it.

“I certainly respect your military experience,” she said. “That’s not what this is about. This is about choosing a president.”

Mr. Buttigieg is campaigning as an antiwar veteran. He is against “endless wars” and in recent days, has attacked Mr. Biden for voting for the Iraq war. “He supported the worst foreign policy decision made by the United States in my lifetime, which was the decision to invade Iraq,” Mr. Buttigieg told the Des Moines public affairs TV program “Iowa Press.”

Veterans represent a relatively small segment of Democratic primary voters, but Mr. Buttigieg uses his status not just as a get-out-of-jail-free card when he is questioned about his experience, but also as a device to connect with voters who may be turned off by candidates from the coasts.