The comments come at a JPMorgan-sponsored event where the outspoken Dimon was answering questions from a moderator about whether he would might be interested in throwing his name in the mix in a 2020 fight for the presidency.
It's impossible to say how Dimon might fare against Trump in a presidential tête-à-tête, but the CEO's company has been the best performers among the nation's largest banks.
Dimon was asked if he thought he could beat Trump in an election during an event to announce a new "Advancing Cities" initiative.
The J.P. Morgan Case boss conceded that he wouldn't fare as well in a Democratic primary. "I should not have said it", he wrote.
Updates to add that White House hasn't yet commented.
'I should not have said it.
"The problem with banker Jamie Dimon running for President is that he doesn't have the aptitude or "smarts" & is a poor public speaker & nervous mess - otherwise he is wonderful", Trump said.
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He said his remarks "proves I wouldn't make a good politician". "I can't beat the liberal side of the Democratic Party", he added, in a reference to his status as a top Wall Street banker. "I am part of the elite", Dimon continued.
"I mean, I've said this before Trump was elected".
In January, Dimon claimed that Democrats can not beat Trump because they don't have a "strong centrist, pro-business, pro-free enterprise [candidate]".
Dimon also took aim at Trump's wealth, saying of himself: "This wealthy New Yorker actually earned his money". "It wasn't a gift from daddy", he said.
By noon, the bank sent out a statement from Dimon, its chairman and chief executive officer, backtracking completely: "I should not have said it". They look at him as the upstart who punched the elite in the nose every day.
Dimon has said while he disagreed with Trump politically he felt it was his patriotic duty to serve on the council.