The death of a former neo-Nazi whose group patrols Arizona’s desert near the Mexican border for illegal immigrants and drug smugglers is raising questions about his organization’s future.

Friends of Jason Todd “JT’’ Ready vowed Friday that U.S. Border Guard’s armed patrols will continue, but monitoring groups doubted the operations could be sustained.

Authorities say the 39-year-old Ready shot and killed his girlfriend and three others, including a toddler, before killing himself in a Phoenix suburb Wednesday, a murder-suicide stemming from domestic violence issues.

The Arizona Republic reported on its website Saturday that the FBI was already conducting a domestic terrorism investigation into Ready’s activities prior to the shootings.

James Turgal, special agent in charge of the FBI’s Phoenix office, told the paper that the FBI’s investigation dated to when Ready was a member of the neo-Nazi National Socialist Movement and continued into his participation with the border group. The probe is based on tips of criminal activity that Turgal would not specify.

He stressed that it had nothing to do with this week’s shootings.

Sean Rose, a 35-year-old Tucson man who said Ready was like a brother to him, said he would quit his job to keep the group going.

“He did a lot for this country as far as protecting the border, something the government doesn’t do,’’ Rose said. “I think it’s good to have civilians stopping the drug market.’’

Groups that monitor the activities of organizations like the U.S. Border Guard expressed doubts that it will be able to maintain its operations. Without Ready’s leadership, they say, the Border Guard will likely disappear.

“The U.S. Border Guard is probably finished,’’ said Mark Potok of the anti-hate group, the Southern Poverty Law Center. “It really did revolve around JT Ready.’’