Trump's comments come less than two weeks after back-to-back mass shootings in El Paso, Texas, and Dayton, Ohio, killed dozens. The suggestions also come a day after a man shot six police officers when he barricaded himself for several hours in his Philadelphia home, where police were attempting to come in with a narcotics warrant.
The emphasis on mental illness -- an approach favored by pro-gun groups -- marked a slight change from earlier this week. On Tuesday, he claimed that many Republicans support his push for strengthening background checks on gun sales -- a view that appears at odds with what lawmakers are telling the President in private.
Trump has said he believes he needs to take a concrete step on gun control, rather than a symbolic one. He's been encouraged by some aides, including daughter Ivanka, to press on background checks.
But others -- including those with more experience dealing with Washington Republicans -- have appeared skeptical. There isn't evidence yet that Trump is wielding an aggressive arm-twisting campaign for a specific piece of legislation as the Senate continues its extended vacation. And an ever-nearing reelection campaign, when support from a gun-loving base will be essential, is likely to weigh on Trump's thinking.
Trump said later Thursday he has been speaking with Senate Majority Leader Mitch McConnell about background checks legislation.
"I've been speaking to everybody about it and we don't want to see crazy people owning guns, but I also want to remember that mental illness is something nobody wants to talk about," he said. "These people are mentally ill and we need to study that also."
"The gun doesn't pull the trigger. They pulled the trigger," he added.
He said he's been speaking to "many Republicans" about the legislation.
"They want to see something happen ... it's very simple. They don't want to have insane people, dangerous people, really bad people having guns. Republicans agree with me on that ... pretty much uniformly," he said.
Trump said he fears Democrats would try to add to the legislation in an unrealistic way, stopping the bill in its tracks.
He wouldn't say whether he supports universal background checks when asked, saying instead, "I support strong, meaningful background checks."
CNN's Kevin Liptak and Kaitlan Collins contributed to this report.