The lawsuit, filed in federal court, accuses the Defense Department of avoiding legal and financial responsibility for the deaths of 13 people and the wounding of more than 30 others by referring to the incident as "workplace violence" rather than a terrorist attack, the Austin (Texas) American-Statesman reported Tuesday.
The victims and families charge the U.S. military knew four years before the shootings that army psychiatrist Maj. Nidal Hasan was an Islamist extremist who supported jihad, suicide attacks and violence.
They accuse federal agencies of bowing to political correctness in ignoring warning signs regarding Hassan.
The group is also suing the estate of U.S.-born Islamic cleric Anwar al-Awlaki. whom they accuse of inspiring Maj Hasan to carry out the attack.
Awlaki was killed by a U.S. drone strike in Yemen last year.
The lawsuit, filed in the District of Columbia, seeks unspecified damages.
Maj. Hasan faces the death penalty if convicted.