WASHINGTON - U.S. President Donald Trump says stricter gun laws in the country would not have prevented a gunman from killing 26 people in a massacre at a Texas church and possibly would have kept a bystander from confronting the shooter.

Trump, in South Korea on a five-nation Asian trip, said Tuesday if there were increased vetting of gun buyers in the United States "you might not have had that very brave person who happened to have a gun or a rifle in his truck go out and shoot him, and hit him and neutralize him."

WATCH: Trump Rules Out 'Extreme Vetting' on Gun Buyers

Asked if he was considering any new gun control policies in the aftermath of the second major mass killing in the U.S. in five weeks, Trump said, "I mean, you look at the city with the strongest gun laws in our nation, is Chicago, and Chicago is a disaster. It's a total disaster. Just remember, if this man did not have a gun or rifle, you'd be talking about a much worse situation in the great state of Texas.”

"And I can only say this: If he did not have a gun, instead of having 26 dead, you would have had hundreds more dead," Trump said. "So that is the way I feel about it. Not going to help."

Air Force probe

Trump made his remarks as the U.S. Air Force investigates why the 2012 domestic violence conviction of the shooter, 26-year-old Devin Kelley, was not properly entered into the Federal Bureau of Investigation's database that would have stopped him from legally buying the rifle he used in Sunday's attack at the First Baptist Church in Sutherland Springs, Texas.

Emergency personnel respond to a fatal shooting at Emergency personnel respond to a fatal shooting at a Baptist church in Sutherland Springs, Texas, Nov. 5, 2017. Emergency personnel respond to a fatal shooting at a Baptist church in Sutherland Springs, Texas, Nov. 5, 2017.

The Air Force had court-martialed Kelley for beating his wife and stepson. He was convicted, sentenced to 12 months in prison, discharged from the military for bad conduct, and handed a reduction in rank. At one point in his confinement, Kelley escaped from a psychiatric hospital in New Mexico, but was picked up by police in neighboring Texas.

WATCH: Who Was the Texas Shooter?

The FBI agent in charge of the investigation in Texas, Christopher Combs, told reporters that Kelley's cellphone has been sent to an FBI laboratory in Virginia for examination, but that so far, because of encryption, investigators have been unable to crack it open to determine whether Kelley made contact with anyone else about the shooting or left any trail of information that he was about to launch the attack.

He declined to name the brand of Kelley's phone so as to not let "bad guys" know how they might possibly be able to hide their criminal activities.

At an earlier news conference Monday, Combs said there was nothing in its data system that prohibited Kelley from buying weapons when a background check was carried out. Kelley passed a federal background check, but the state of Texas denied him a permit to carry a gun.

Combs refused to say Kelley's name, saying he did not want to glorify him. Combs would only call him "the gunman." Combs said "horrific" is too weak a word to describe the scene inside the First Baptist church. In addition to the 26 killed, 20 others were wounded.

Texas public safety official Freeman Martin said as of Tuesday, 10 of the victims remain in a hospital in critical condition.

The youngest fatality was 18 months old. A pregnant woman was also killed.

Domestic dispute

Martin, who also refused to use the gunman's name, said the shooter came to the church with a purpose and a mission.

Investigators say they believe a domestic dispute with his in-laws appeared to have been behind the killings. Kelley sent "threatening texts" to his mother-in-law before the shooting, investigators said, but she was not at Sunday's service.

"He was upset with the mother-in-law, but beyond that I can't comment," Martin said.

"This was not racially motivated ... wasn’t over religious beliefs. There was a domestic situation going on within the family and in-laws,” Martin said.

Kelley was dressed in black and wore a skull mask. He opened fire outside the church with a Ruger 556 assault rifle and kept shooting when he went inside the building.

He was confronted by a church neighbor, Stephen Willeford, who was armed with his own rifle. Kelley fled the scene, with Willeford in pursuit in a high-speed chase in the truck of a man, Johnnie Langendorff, who happened to drive by as the mayhem unfolded. They were soon joined by police.

Willeford told a Texas television station, "He saw me and I saw him. I was standing behind the pickup truck for cover. It was surreal to me that it could be happening. I could not believe it."

Willeford exchanged gunfire with Kelley. "I know I hit him. I don't know where I hit him," Willeford said.

Stephen Willeford, right, and Johnnie Langendorff, Stephen Willeford, right, and Johnnie Langendorff, left, attend a vigil for the victims of the First Baptist Church shooting in Sutherland Springs, Texas, Nov. 6, 2017. Stephen Willeford, right, and Johnnie Langendorff, left, attend a vigil for the victims of the First Baptist Church shooting in Sutherland Springs, Texas, Nov. 6, 2017.

The chase ended when Kelley crashed his car and shot himself in the head. He died at the scene. Martin said he had two other bullet wounds from the shots fired by Willeford.

The gunman telephoned his father as he sped from the church, telling him that he had been shot and did not expect to survive.

Kelley fired a total of 450 rounds at the church, authorities said.

Governor responds

Texas Governor Greg Abbott told CBS News, "It's clear this is a person who had violent tendencies, who had challenges. Someone who was a powder keg waiting to go off."

The deadly mayhem in Texas came a month after the worst mass shooting in U.S. history, when a man named Stephen Paddock opened fire on a country music show in Las Vegas, killing 58 and wounding about 500. Paddock shot from his 32nd floor hotel room and killed himself as police zeroed in. Investigators are still looking for a motive.

Marie Ann Montgomery, the church's Sunday school director, said people in the congregation knew the gunman. Among those killed was a grandmother of Kelley's wife.