Naked except for a green jacket, he then fled, and he remained at large as of Sunday night. The police said murder warrants were being drafted.
Don Aaron, a spokesman for the Metropolitan Nashville Police Department, said at a news conference on Sunday that after leaving the restaurant, Mr. Reinking shed his jacket. In it were two magazines of AR-15 ammunition.
The police credited a customer with averting further bloodshed. The customer, James Shaw Jr., 29, seized the moment when he saw Mr. Reinking apparently trying to reload his rifle. Mr. Shaw burst out from behind a swinging door where he had been hiding, wrested the weapon away and threw it over a countertop.
“I kind of made up my mind, because there was no way to lock that door, that if it was going to come down to it, he was going to have to work to kill me,” Mr. Shaw said at the news conference.
Mr. Reinking fled on foot, and apparently returned to his apartment nearby to put on pants. He was last seen shirtless and shoeless, Police Chief Steve Anderson said. Investigators had yet to determine a motive for the killings.
Officials could not fully explain how Mr. Reinking regained possession of his weapons after they were taken away following his episode near the White House last year.
Federal authorities worked with county officials in Illinois to investigate Mr. Reinking. The Tazewell County Sheriff’s Office in Illinois gave the weapons he owned — including the AR-15 he brought to the Waffle House on Sunday — to his father.
Sheriff Robert M. Huston of Tazewell County said in a news conference on Sunday that while Mr. Reinking “voluntarily surrendered” the weapons on Aug. 24, his father had a firearm owner’s identification card and a legal right to take the weapons.
“He was allowed to do that after he assured deputies that he would keep them secure and away from Travis,” Sheriff Huston said. “We have no information about how Travis came back into possession of those firearms.”
The police in Nashville indicated that Mr. Reinking’s father returned the weapons to his son. The father, Jeffrey Reinking, could not be reached for comment on Sunday.
Even before he went to Washington, Mr. Reinking had a history of encounters with law enforcement in Illinois.
According to one sheriff’s report from May 27, 2016, he “was delusional and believed the famous entertainer, Taylor Swift, was harassing him via stalking and hacking his phone.” It added that he said he found Ms. Swift at a Dairy Queen in Morton and chased her before she disappeared.
Mr. Reinking’s family members said he had had these delusions since August 2014. The report noted that “Travis is hostile towards police and does not recognize police authority.”
In another episode on June 16, 2017, in Tremont, Ill., the police responded to a complaint that Mr. Reinking, wearing a woman’s pink housecoat, jumped into a pool and began arguing with lifeguards to get them to fight with him. No one at the pool wanted to press charges, the report said.
Mr. Reinking’s attempt to meet with the president came one month later.
Mr. Aaron said Mr. Reinking was believed to have moved to Nashville in the fall and worked in the crane and construction industries. Mr. Reinking was fired from a job about three weeks ago and found a new job, Mr. Aaron said, but had not been seen at work since Monday.
The authorities said Mr. Reinking could still be in possession of a handgun and a rifle, which Chief Anderson described as “more of a hunting-type rifle than an assault rifle.”
The Nashville police identified the four people who died as one Waffle House employee, Taurean C. Sanderlin, 29; and three customers: Joe R. Perez, 20, of Nashville; Deebony Groves, 21, of Gallatin; and Akilah Dasilva, 23, of Antioch.
Jennifer Wetzel, a spokeswoman for Vanderbilt University Medical Center, said one wounded victim was in critical condition and another was in critical but stable condition. Two other victims were treated for minor injuries and discharged from TriStar Southern Hills Medical Center in Nashville, said Katie Radel, a spokeswoman there.
Waffle House restaurants are open 24 hours and speckled throughout the South, especially along the interstates.
The gunfire on Sunday was the latest burst of violence at one of the chain’s outposts. In January, an altercation at a Waffle House in Missouri turned fatal when a security guard opened fire. And a deadly shooting outside a location in Florida that same month recently led to a lawsuit.
Still, Sunday’s attack was especially jarring in its method and magnitude.
Walt Ehmer, the company’s chief executive, said it was a “very sad day” and thanked Mr. Shaw. “You are a hero,” he said. “You’re my hero.”
But Mr. Shaw demurred. “I’m not a hero,” he said, adding that he acted out of self-preservation.