But while he would have been eligible two or three times before he retired to be placed in charge of a unit as a commanding officer, he never was. And without serving as a commanding officer, he could not become a captain, which is equivalent to a colonel in the other services, and then an admiral, as some of his SEAL peers have.

Kenneth Stethem, a retired SEAL chief petty officer who supports Mr. Zinke, said the travel issue seemed minor so many years later. “We have a saying in the teams: ‘You never shoot a high-caliber man with a low-caliber bullet,’ and that’s exactly what’s going on right here,” he said.

But some former SEAL team members claim that Mr. Zinke has also exploited his past — he placed the SEALs’ insignia (with six stars, presumably for SEAL Team 6) on his campaign bus in violation of Defense Department guidelines against politicizing such symbols — and that he exaggerated what he did in his later military jobs to obscure that he never received commands of his own.

He published an autobiography in November that was grandly titled “American Commander.” And his biography on his congressional website says that he was “deputy and acting commander” of a task force “where he led a force of over 3,500 Special Operations personnel in Iraq” in 2004.

In an interview, Michael S. Repass, who retired from the Army as a major general and was Mr. Zinke’s boss in Iraq, chuckled and said, “That might be a stretch.” General Repass said that while Mr. Zinke was his deputy commander for four months, he had named him acting commander for only about a week and a half, when the general traveled to the United States.

General Repass said Mr. Zinke “did a good job” as his deputy and was “a competent guy,” and he had nominated Mr. Zinke for one of two Bronze Stars he received. Admiral Pybus said that Mr. Zinke was “embarrassed and humbled” when he left SEAL Team 6 and “did quite well” as his deputy at a command using less-elite SEAL units in Europe.

“I didn’t see any fallback on poor judgment or indiscretions,” Admiral Pybus said, adding that he had heard Mr. Zinke also did well in another Navy job, as the second-ranking officer (and briefly acting commander) of the main SEAL training center.