Mr. Wood said he had initially hoped to attract about 500 veterans; he had to stop sign-ups when they reached 2,000. He said volunteers are from diverse backgrounds: “We have every age, we have every war.”

An online fund-raiser has drawn over $570,000 in pledges as of Tuesday afternoon to pay for food, transportation and supplies for the veterans’ “muster,” which was planned for Dec. 4-7.

One veteran, Loreal Black Shawl, said the mission to support the protesters was intensely personal.

Ms. Black Shawl, 39, of Rio Rancho, N.M., is a descendant of two Native American tribes, the Oglala Lakota and Northern Arapaho. She served in the Army for nearly eight years, finishing her career as a sergeant.

“O.K., are you going to treat us veterans who have served our country in the same way as you have those water protectors?” Ms. Black Shawl said, referring to the protesters. “We’re not there to create chaos. We are there because we are tired of seeing the water protectors being treated as non-humans.”

The authorities have used rubber bullets, pepper spray and water cannons against demonstrators, hundreds of whom have been injured, according to protest organizers. The clashes have been highly contentious, with the police and demonstrators leveling accusations of violence at each other.