Minneapolis Fed President Neel Kashkari is taking on the financial world's perhaps most well-known and powerful name — JPMorgan Chase CEO Jamie Dimon, whom the central bank official said recently made "demonstrably false" statements about the industry.

In his annual letter to investors, Dimon said "too big to fail" fears have been eradicated. The expression stems from the financial crisis, when taxpayers were on the hook for billions in bailouts to the financial industry. Dimon contended that banks are well-capitalized and well-regulated enough to sustain shocks similar to what happened during the crisis.

Kashkari disputed both points. He said bank equity won't be near enough to help the industry in the case of another crisis, and believes regulators are still being too easy on banks.

"Although capital standards are higher than before the last crisis, they are not nearly high enough," Kashkari said in a blog post on Medium.com. "The odds of a bailout in the next century are still nearly 70 percent."

A Fed analysis concluded that banks should be able to able to handle a 20 percent loss on assets during a crisis. To get to that level, bank capital standards should be doubled from current levels, Kashkari said.

Officials at JPMorgan did not immediately respond to a request for comment.