The Albuquerque Journal reports the exemptions are based on high unemployment rates.
Counties being excluded from the rules include Luna as well as McKinley and Mora, and the tribes and pueblos being exempted include the Navajo Nation.
In August, Luna County once again had the highest unemployment percentage in the state at 12.8%, followed by Mora with 12.4%, and McKinley with 10.1%.
Luna County consistently has double-digit unemployment.
The new Human Services Department rules to re-impose work requirements for food stamp nutrition assistance are scheduled to start taking effect November 1st in three planned phases.
Counties in the first phase include Bernalillo, Sandoval, Santa Fe and Valencia.