FBI agents work the scene at the Armed Forces Career Center in Chattanooga, Tennessee, July 16, 2015. [Photo/Agencies]

Meanwhile, Reinhold said that the gunman, with "numerous weapons" on him, did not work at the military facilities involved.

The shooting incidents came one month after a racially motivated white gunman shot dead nine African-American churchgoers in Charleston, South Carolina. The authorities were initially investigating the Charleston church massacre as "hate crime," rather than a possible act of terrorism.

Thursday's shootings also came at a time when US military and law enforcement officials were increasingly concerned about threats posed by domestic sympathizers of the extremist group the Islamic State. The group had earlier called on its supporters to carry out lone-wolf attacks against "its enemies" worldwide during the month of Ramadan.

The Washington Post earlier quoted senior FBI officials as saying that the shooting did not appear to be related to any terrorist group.