The Army’s Special Operations Command at Fort Bragg, N.C., announced the exercise in March, saying that while a multistate training operation was not unique, “the size and scope of Jade Helm sets this one apart.” Jade Helm 15, according to military officials, amounts to a giant war game spread across the Southwest, with Army Green Berets and other elite personnel sharpening their skills in terrain they might find overseas.

Army officials said the operation would not be conducted at Fort Hood, the sprawling base in Killeen, Tex., but instead would take place in remote areas on “private and public land with the permission of the private landowners, and from state and local authorities.” They said the most noticeable effect on local communities will be “an increase in vehicle and military air traffic and its associated noise.”

Mr. Abbott’s directive has touched off a wave of condemnation and support, with some blasting him for giving conspiracy-minded activists an air of respectability and others saying that they, too, were concerned about federal military drills on Texas soil.

Residents in rural Bastrop County packed a community meeting last week about the plans for the military exercise. On Tuesday, Representative Louie Gohmert, a Republican, called for changes to the exercise, particularly a war-simulation map that labels Texas, Utah and part of Southern California as “hostile.” He said that because the Obama administration believed “that major threats to the country include those who support the Constitution, are military veterans or even ‘cling to guns or religion,’ patriotic Americans have reason to be concerned.”

A leader of the Republic of Texas, a separatist group that believes Texas never officially joined the United States, forwarded an email to reporters in which an anonymous man claiming to be a Texas Ranger wrote that Texans “should be pushing back against JH15.”

Chuck Norris has also weighed in, questioning, in a commentary on the conservative website WND, “those who are pulling the strings at the top of Jade Helm 15 back in Washington.” Walmart has responded as well, in the other direction — it dismissed rumors that tunnels were being built by the military beneath closed stores, including one in Midland, Tex., as part of a Pentagon-led takeover.