Dimon: I wouldn't have left If I lost leadership vote

Jamie Dimon told CNBC on Friday he would have stayed at JP Morgan Chase even if his chairman and CEO roles had been split, despite reports that he had planned to leave.

"I wouldn't have liked it, but I never would have left my company high and dry," Dimon said of the vote in May.

(Read More: JPM Averts CEO/Chair Job Split, in Boost to Dimon)

In a wide-ranging interview, he also told CNBC's "Squawk on the Street" the banking giant can do well even in a rising interest rate environment, despite what that may do to mortgage rates, as long as the overall economy is doing well.

"All things being equal, rates going up is a good thing, as long as the economy is growing," he said when asked about the Federal Reserve's eventual plan to taper bond purchases.

"We all want normalized rates. I believe in the process of normalization you're going to have some volatility," he said. "Look past the volatility. As long as the economy is strong, I think we're going to be fine."

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One portion of the business that Dimon thinks JP Morgan could improve on is mortgage servicing.

Wells Fargo does "a lot better in the mortgage business than us. They have been doing better for a long time," Dimon said in the interview with Jim Cramer. "At the end of the day we're going to have a great mortgage business. We're going to be really good at servicing, we just have a little more wood to chop."

The interview came a day after a bipartisan group of senators, including Sens. Elizabeth Warren and John McCain, introduced legislation that would break up Wall Street's megabanks by separating traditional banking activity from riskier financial services.

(Read More: Elizabeth Warren Pushing Bill to Break Up Big Banks)

All banks have to adjust to the regulatory environment in the U.S. and globally, Dimon said. "Eventually, we'll be back to business as usual. That may take another year or two."

Regulation, he said, will eventually "determine how aggressively banks will grow, how aggressively they can pay dividends and return capital."

Earlier Friday, JP Morgan said profit surged in the second quarter by 31 percent, based on a rebound in trade revenue. Net income rose to $6.5 billion, or $1.60 per share, in the second quarter ended June 30 from $4.96 billion, or $1.21 per share, a year earlier. JPMorgan also set aside less money to cover bad loans.

More on JPM's Earnings:
JPMorgan Slays 'Whale' in 2nd Quarter as Profit Surge
Wall Street Doesn't Like the Way JP Morgan Beat

The company also reported that it generated a total of $1 trillion in raised capital and extended credit during the first six months of 2013. Of the extended credit, $9 billion went to small businesses and $294 billion to large corporations.

"Small business has not completely recovered like large companies have," he said. "I think that small business will recover with the economy. When the economy starts to grow, you're going to see small businesses take off and their credit needs grow."

America has a "gift from god" in its economy and the country "is going to come back, and it's going to blow people's socks off when it does."

The economy "is strengthening, it's very broad-based," he said. "There is almost no sector—large company, middle market company, small business, consumers, housing—there's nothing that's not getting a little bit better."

"If we're a little bit lucky and we get a little back-wind next year from the fiscal side, you may see stronger growth in America."

Dimon's prediction for America in 2014: "GDP will be stronger and unemployment will be at 6.5 percent."

— By CNBC's Paul Toscano, with Reuters. Follow Toscano on Twitter and get the latest stories from "Squawk on the Street" @ToscanoPaul.

Jim Cramer's Charitable Trust owns shares of JP Morgan