At a press conference Monday morning, Trump was asked what he thinks about the case, and the reaction to it -- including the adoration of many online for the suspected killer, Luigi Mangione, who was arrested in Pennsylvania last week.

Trump said ... "I think it's really terrible that some people seem to admire him, like him."

As TMZ reported, there's been a huge reaction online across the country in support of Mangione, and against Thompson and other CEOs of healthcare companies -- prompting increased security for some executives. A wave of merchandise supporting Mangione was pulled from Etsy and other sites, and at least one online funding campaign was also taken down.

"I was happy to see that it wasn't specific to this gentleman that was killed, it's just an overall sickness as opposed to a specific sickness," Trump said Monday at his Mar-a-Lago property in Florida. "Just a cold-blooded horrible killing -- and how people can like this guy is -- that's a sickness, actually, that's really very bad."

Trump went on, "A thing like that, you can't believe that some people -- and maybe it's fake news, I don't know -- it's hard to believe that that can even be thought of."

Filmmaker Michael Moore offered his thoughts on the case after it was revealed he was name-checked in a purported manifesto found in Mangione's possession when he was arrested ... allegedly detailing his anger at healthcare in the United States. Moore does not excuse the murder ... but he says he understands the public reaction to the problems of the American healthcare system, writing "The anger is 1000% justified."

Comedian Chris Rock addressed the case and its controversies on "Saturday Night Live" this weekend, cracking a couple jokes about Mangione, then expressing support for the victim's family ... before dropping a zinger about the shooting.