Stricter gun controls could have resulted in more deaths during the Texas church shooting massacre because a neighbor might not have been able to shoot the gunman, President Trump said Tuesday.

Trump, speaking at a news conference in South Korea, was asked if he would be willing to use "extreme vetting" for people who want to buy a gun, similar to the "extreme vetting" he has discussed for people coming to the United States.

Trump replied that stricter gun controls would have made "no difference" in the carnage Sunday at the First Baptist Church in Sutherland Springs, Texas. Devin Kelley, 26, fatally shot 26 people and wounded 20 more during a service at the rural church outside San Antonio.

Trump added that stricter gun controls might have kept Stephen Willeford, who lived near the church, from intervening in the massacre.

"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," Trump said. "If he didn't have a gun, instead of having 26 dead, you would have had hundreds more dead."

Trump went on to say that Chicago has the strictest gun laws in the nation, and "Chicago is a disaster."

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In Washington, House Speaker Paul Ryan, R-Wis., was asked Tuesday what his recommendations would be to prevent gun violence.

"How about enforcing the laws we have on the books?" Ryan said. "If you’re a domestic abuser, you’re not supposed to own a gun. He (Kelley) was a domestic abuser. That’s why we got all these questions with the Air Force right now which is ‘How did this slip through the cracks?’”

Kelley had a history of domestic violence and escaped a mental health facility in 2012. The Air Force acknowledged that officials at Holloman Air Force Base in New Mexico failed to enter Kelley’s domestic assault conviction there into the National Criminal Information Center database.

"Domestic violence convictions would have prohibited Kelley from making firearm purchases, but the information was never received for use in any of the three databases,” the FBI said said in a statement.

The Air Force and the Pentagon's Inspector General have launched investigations to determine what happened.

Vice President Mike Pence is scheduled to visit Sutherland Springs on Wednesday. Senate Majority Whip Steve Scalise, R-La., who was critically injured during a shooting this summer at a GOP baseball practice outside Washington, sent his condolences.

“My prayers remain with the people of Sutherland Springs," he said. "I know what they’re going through and I know how important the power of prayer is and how important for them to know that all of us are lifting them up in our prayers during this difficult time.”

Authorities say Kelley fired more than 400 rounds. Texas Department of Public Safety official Freeman Martin said Kelley sent threatening texts to his mother-in-law, a member of the church, before the attack. But the woman was not at the church when the bloodshed took place.

FBI Special Agent Christopher Combs said the FBI has Kelley's phone but thus far as been unable to crack into its contents, a growing problem for investigators across the nation, he said.

"We are working very hard to get into the phone," he said. "It could be tomorrow, it could be a week, it could be a month."

In Sutherland Springs, Willeford is being hailed as a hero. He was in his home when his daughter told him a shooting rampage was underway at the nearby church, Willeford told 40/29 News TV. He said he loaded his magazine and ran across the street to the church, not even taking the time to put on shoes.

Willeford saw the gunman outside the church, and the two exchanged gunfire.

"He saw me and I saw him," Willeford said in the TV interview. "I was standing behind a pickup truck for cover."

Police say Kelley was shot twice and fled in his SUV. Minutes later he called his father, telling him he was shot and wouldn't survive. The car crashed, and he was found dead. Police say Willeford shot Kelley in the leg and torso, and Kelley shot himself in the head.

Willeford says he is no hero.

"I think my God, my Lord protected me and gave me the skills to do what needed to be done," Willeford said.

Contributing: Eliza Collins, John Moritz