Minneapolis Federal Reserve President Neel Kashkari told CNBC on Friday banks need "about twice as much" rainy-day capital to effectively address "too big to fail," which put U.S. taxpayers on the hook to bail out Wall Street firms during the 2008 financial crisis.

Higher capital requirements would be on "the biggest banks, only the biggest banks" to guard against the "contagion risk" of a cascading collapse in the financial system, he said on "Squawk Box."

He said he's talking about banks with "$250 billion in assets and up. That's about a dozen banks in America."

"Those are the 'too big to fail' banks as we see it," he said.

In a blog post Thursday , Kashkari argued that JPMorgan Chairman and CEO Jamie Dimon recently made "demonstrably false" statements about the banking industry.

Dimon, in his annual letter to shareholders this week, wrote "too big to fail" fears have been eradicated. He contended banks are well-capitalized enough to sustain shocks similar to what happened during the financial crisis.

Kashkari disputed Dimon's comments, saying on CNBC: "This is nothing personal. ... Banks don't have nearly enough capital."

"The biggest banks need about twice as much equity capital as they have today," he continued. "We could more or less address 'too big to fail.' We haven't done it yet."

Addressing critics who argue that higher capital requirements would keep banks for lending and hurt the economy, Kashkari said, "This is about analyzing costs and benefits.

"The benefits of higher capital are we avoid these disastrous financial crises," he said. "Safety isn't free."

Kashkari said he'd be willing to accept a little less lending from the big banks because "the benefits outweigh the costs."