In a tweet, Trump also boasted: "I've made a lot of bankers, and others, look much smarter than they are with my great economic policy!"
Dimon made his impromptu comments at an event at the bank's Park Avenue headquarters in New York.
"I think I could beat Trump," Dimon said. "Because I'm as tough as he is, I'm smarter than he is. I would be fine. He could punch me all he wants, it wouldn't work with me. I'd fight right back."