Dimon added that people at the lower end of the spectrum have "particularly been left behind," noting: "We haven't done a good job growing our economy. That would've fixed a lot of that problem."

"I think it's a huge problem," Dimon said. "I think the wealthy have been getting wealthier too much in many ways, so middle class incomes have been kind of flat for maybe 15 years or so, and that's not particularly good in America."

His remarks come amid increased criticism of the rich by certain U.S. presidential hopefuls, particularly Democratic Sen. Elizabeth Warren from Massachusetts.

I think you should vilify Nazis, but you shouldn't vilify people who've worked hard to accomplish things.

On Oct. 23, Warren called in a tweet for billionaire investor Leon Cooperman to "pitch in a bit more so everyone else has a chance at the American dream." The tweet drew the Cooperman's ire.

Cooperman sent a letter to Warren's office in late October, saying "your tweet demonstrated a fundamental misunderstanding of who I am, what I stand for, and why I believe so many of your economic policy initiatives are misguided."

He then told CNBC's "Halftime Report" on Nov. 4 the "vilification of billionaires makes no sense to me." When asked why he spoke out against Warren, a tearful Cooperman said, "I care."

Warren responded to Cooperman's remarks by tweeting: "One thing I know he cares about—his fortune." She then criticized Cooperman's investments in student-loan company Navient and said she cares "about an entire generation of students being crushed by student loan debt."

@ewarren: I care about an entire generation of students being crushed by student loan debt—deferring their American dream because they can't afford it. I care about making sure every American has the opportunity to succeed. I'm not afraid to stand up to the wealthy and well-connected.

But while J.P. Morgan's Dimon is worried about growing wealth inequality — a Credit Suisse report from last month said millionaires now hold 44% of the world's total wealth — he reprimanded Warren and others for their criticisms of the wealthy.

"Anything that vilifies people, I just don't like. I think that most people are good; not all of them," Dimon said in the Sunday interview. "I think you should vilify Nazis, but you shouldn't vilify people who've worked hard to accomplish things."

Dimon also deflected questions about him making $31 million in 2018. He said J.P. Morgan Chase's board of directors sets his salary and "I have nothing to do with it."

@60Minutes: "Last year, you were paid $31 million. Too high?" JPMorgan Chase Chairman and CEO Jamie Dimon says he thinks the wealth gap in America is a "huge problem," but he passed the buck when asked about his salary. https://cbsn.ws/32uoTYU

He reiterated, however, that there are solutions to wealth inequality, such as changing the U.S. miniumum wage and lowering taxes for the poor and the middle class. "The problems are real, it does not mean free enterprise [is] bad."