“The conditions in the Navajo Nation are akin to a third world country,” Mr. Deschene said. In an interview, he repeatedly stressed the importance of preserving language and culture, but added, “Our job as leaders is to provide for the basic needs of our people. Every member of the nation deserves basic amenities like water, power and roads.”

If Mr. Deschene stays on the ballot, he will face Joe Shirley Jr., a former Navajo Nation president. Mr. Shirley, 66, said that preserving the tribe’s traditions would be his top priority if he were elected again.

“Preservation of our way of life and our culture is foremost, and fundamental to us,” Mr. Shirley said. “Five hundred years down the road, I want people to be speaking the language, and have our way of life.”

On the red mesas at the western edge of the reservation, Jack Begay, 56, bemoaned the shrinking population of Navajo speakers like himself.

“A lot of our young, they don’t really care to talk Navajo,” said Mr. Begay, a rancher who herds cattle, horses and sheep. “We’re forgetting more and more our culture.”

Even so, he said, he supports Mr. Deschene, saying that past presidents had done little for the western part of the Navajo Nation. “He’s new, and he’s been in the military — that will help,” Mr. Begay said. “We teach our kids to go out and get an education, and maybe one day come back and lead the Navajo people. That’s what Chris did. He went to college, and now he’s back to the Navajo people.”

For now, the Navajo language remains prevalent on the reservation, heard in casual exchanges at variety stores as well as at the Navajo Supreme Court hearing on Friday. While most of the arguments were conducted in Navajo, Mr. Deschene spoke largely in English, arguing that the law requiring the president to speak Navajo was discriminatory and did not “invite a new generation of leaders to participate.”