Federally licensed gun shops must use the National Instant Criminal Background Check System, or NICS. Private sellers and gun shows have no background check requirement.
But information in the national background check system is incomplete, particularly involving mental health records, investigations have found.
Critics blame what they call a huge legal loophole, according to one study.
"PTSD is rarely associated with homicidal violence," Michael Welner, a forensic psychiatrist who has worked on cases of Iraq and Afghanistan veterans charged with violent crimes, told CNN's Soledad O'Brien.
"PTSD is very commonly associated with a number of other conditions that are regularly attached to violence, alcoholism, personality disorder, depression. So diagnostically, PTSD may be relevant and it may just be part of the picture, including traumatic brain injury," Welner said.
Expanding some background checks is under consideration in Congress as lawmakers respond to public and political pressure for stricter laws following December's shooting massacre at a Connecticut elementary school.
Possible steps include better monitoring of people with mental illness to prevent them from obtaining firearms.
Mayors Against Illegal Guns aired an ad during the Super Bowl advocating universal background checks for gun sales.
President Barack Obama also reiterated his call on Monday for comprehensive steps to address gun violence, including expanded background checks.