The Metro Nashville Police Department said Travis Reinking, 29, was last seen on Sunday morning behind his apartment complex.
“There have been no credible sightings. The search will continue. All schools in the area have been cleared by officers,” the department said in a statement.
Metro Nashville Public Schools said as the manhunt continued, it would operate a “lock-out” — meaning no guests or visitors allowed — at schools in the southeastern suburb of Antioch, where the Waffle House restaurant is located, and nearby Cane Ridge.
Authorities confirmed that Taurean Sanderlin, 29, Joe Perez, 20, and Deebony Groves, 21, were shot dead at the restaurant at 3:25 am (0825 GMT) Sunday.
The fourth victim, 23-year-old Akilah Dasilva, died in hospital, while two others were injured.
Police identified Reinking, originally from Illinois, as the suspect, warning he could be armed with a rifle and a handgun, after firing an AR-15 semi-automatic rifle at the restaurant, where he was nude except for a green jacket.
They said they believed the gunman discarded the jacket while fleeing to his home, where he put on a pair of pants and then disappeared into nearby woods.
Before fleeing the scene, the shooter was disarmed by 29-year-old James Shaw, who was celebrated as a hero after grabbing the gun and getting the suspect outside following a scuffle.
“You don’t get to meet many heroes in life, Mr Shaw, but you are a hero. You are my hero. You saved people’s lives,” Waffle House CEO Walt Ehmer told him Sunday. DM