"This isn't a gun problem, this is a mental problem," Trump told CNN's Chris Cuomo on "New Day." "It's not a question of the laws, it's really the people."
Calling the gunman a "very sick man," Trump said mental illness is "a massive problem" in the U.S. He suggested more resources should be devoted to addressing mental health -- hoping to prevent shootings like the one in Virginia, which he called "really, very sad."
Trump did not offer specific solutions to addressing the mental health problem, but said there are '"so many things that can be done" and repeatedly said the Virginia shooter
, who killed himself Wednesday after killing two others
, should have been "institutionalized."
"In the old days they had mental institutions for people like this because he was really, definitely borderline and definitely would have been and should have been institutionalized," Trump told Cuomo. "At some point somebody should have seen that, I mean the people close to him should have seen it."
Gun control advocates once again pressed for reforms in the wake of Wednesday's tragedy, with President Barack Obama calling the shooting "heartbreaking" and "one more argument for why we need to look at how we can reduce gun violence in this country."
"What we know is that the number of people who die from gun-related incidents around this country dwarfs any deaths that happen through terrorism," Obama said, as his spokesman Josh Earnest earlier in the day reaffirmed Obama's plea for "common sense" gun legislation.
Hillary Clinton also made a similar case on Wednesday. On Thursday, she tweeted: "We are smart enough -- compassionate enough -- to figure out how to balance legitimate Second Amendment rights with preventive measures."
But Trump insisted Thursday that changes in the nation's gun laws were not the solution needed, saying he is "a very strong Second Amendment person."
And he insisted it should not be more difficult for "sane people" to get guns, pointing to Chicago's tough gun laws failing to prevent the scourge of gun violence in that city.
Again, Trump pivoted to mental health.
"I guarantee you there are a couple of people that knew this man that did the killing yesterday that probably said, 'Wow he's really got problems I mean he really should be institutionalized,'" Trump said.
Trump also praised the reaction of the journalists' colleagues, who continued to broadcast live throughout the day on Wednesday.
"The reaction of the colleagues and the station has been really incredible and it's really inspiring to watch," Trump said. "It's too bad that we can't figure it out beforehand, but it's a pretty tough thing to do."