(CNN) Secretary of Defense Lloyd Austin denied a request from Oklahoma's governor to exempt his state's National Guard members from the Pentagon's Covid-19 vaccine mandate.
Austin emphasized that the vaccine mandate is a lawful order that promotes "the health, safety and readiness of our military personnel, regardless of duty status" in the letter, which CNN obtained a copy of.
The letter added that National Guard members who don't get vaccinated could be banned from "participation in drills and training conducted," and their status in the service could be jeopardized.
But Oklahoma Gov. Kevin Stitt didn't appear ready to back down. In response to Austin's letter, a spokesman for Stitt said the governor "appreciates" the letter but "maintains his position that the governor is commander in chief for all members of the Oklahoma National Guard while they are on" state orders.
In early November, Stitt sent a letter to Austin asking him to suspend the vaccine requirements for the Oklahoma National Guard. He said the mandate "violates the personal freedoms" of guard members and potentially requires them to "sacrifice their personal beliefs."
Austin rejected these arguments. "The concerns raised in your letter do not negate the need for this important military readiness requirement," the defense secretary wrote.
The argument about the vaccine requirement led to a dispute about the limits of the federal government's authority and the military chain of command.
Stitt ordered Brig. Gen. Thomas Mancino, the newly appointed head of the Oklahoma National Guard, not to enforce the vaccine mandate. Mancino, who acknowledged it put him in an awkward situation, said that under state orders, his commander was the governor. But he also said that if the guard were called up under federal orders, called Title 10, he would enforce the vaccine requirement.
A defense official who briefed reporters on the issue said that members of a National Guard unit, even under state orders, called Title 32, are still required to meet federal mission requirements, including medical requirements such as vaccine mandates.
Guard members who refuse to get vaccinated risk losing their status in the National Guard and the federal pay that comes as part of training, drills and more.
Both Title 32 and Title 10 are paid for by the federal government, not the states.
Pentagon spokesman John Kirby said no other governors have made similar requests during a briefing at the Pentagon on Monday.
Kirby reiterated points Austin made in the letter, saying not getting vaccinated could put National Guard members at risk of losing their status.
"So one could elect not to take the vaccine of course but then you would be putting at jeopardy your ability to stay in the national guard, which as you know is also a component of the reserve component in the total force," Kirby said. "But in the specifics of how that would play out, I'd refer you in this case specifically to the Oklahoma National Guard to speak to."
CORRECTION: An earlier version of this article gave the wrong title for Lloyd Austin. He is the secretary of defense.
This story has been updated with background and further details.