"When you suffer from a pathological disease, you're not really getting better unless you start taking pills or something," Trump told Fox News' Bill O'Reilly of Carson, who has described his childhood anger and temper as "pathological." "Do you think that's the right temperament to be president? I don't think so."
Trump added that he did not think questions about Carson's past were "small ball," casting aspersions on his presidential rival's backstory.
"There's something very strange here. Something very strange is going on," he said.
Trump's comments came a day after he questioned the narrative of Carson's rough upbringing, when he said the retired neurosurgeon's previous accounts could be a "total fabrication."
"The Carson story is either a total fabrication or, if true, even worse-trying to hit mother over the head with a hammer or stabbing friend!" he tweeted Thursday evening.
Carson aggressively pushed back Friday against media reports about his past.
"There is a desperation on behalf of some to try to find ways to tarnish me because they've been looking through everything, they have been talking to everybody I've ever known, everybody I've ever seen," Carson told reporters at a media availability in Florida.
Trump and Carson, the two national Republican front-runners, have largely bonded together over the course of the campaign, most recently using their leverage to try and force changes to the debates organized by the Republican National Committee. But as Carson has surged, Trump has increasingly been willing to criticize Carson -- even though Carson has not done the same to Trump.
Trump's comments follow a CNN report published earlier Thursday that probed the retired neurosurgeon's descriptions of his violent past. Carson has said he attacked a boy named Bob with a knife and hit another child named Jerry with a lock. Carson said Thursday that those names weren't real, and that the person he once tried to stab was an unidentified "close relative."
So far, the real estate mogul has stood alone among GOP presidential contenders in criticizing Carson over CNN's report. On Friday, New Jersey Gov. Chris Christie told CNN's Jake Tapper on "The Lead" that Carson "will answer any questions that anyone might have about his personal story, and then the voters will decide whether that answer is good enough or not."