Wells Fargo (WFC) Chief Executive Officer John Stumpf said managing low interest rates may be the most pressing challenge for bankers and that his company had prematurely kept funds idle to gird for increases.

"One of the biggest risks today in our industry is not credit risk, its interest-rate risk," Stumpf said today at an investor conference in New York sponsored by the Sanford C. Bernstein & Co. research firm.

Investors have pressed bankers on how their firms can increase lending profit margins in a low-rate environment and drive up stock prices. Some banks have been wary of taking on business with rates hovering near record lows on concern loans will become less valuable when more-normal conditions return. Wells Fargo, based in San Francisco, is the largest U.S. home lender and ranks fourth by assets.

"We've probably been wrong the last couple years, we've had a lot of this stuff on the sidelines saying rates will turn around sometime," Stumpf said. "Well, sometime hasn't come yet."

That may finally be changing, Stumpf said, citing a recent rise in rates on concern that the Federal Reserve will slow debt purchases as the economy gains speed. Corporate notes denominated in dollars declined 0.7 percent on May 28, erasing gains for the year as 10-year U.S. Treasuries posted the biggest one-day decline since October 2011, Bank of America Merrill Lynch index data show.

Cutting credit losses and boosting the firm's vast pool of inexpensive deposits will assist Wells Fargo's profit margins, Stumpf said. He wants to increase loans from $800 billion to about $1 trillion, closer to matching its deposits, he said.

Stumpf said he doesn't consider Wells Fargo too big to fail and that more restrictions aren't needed. Lawmakers who argue that the Dodd-Frank Act hasn't safeguarded taxpayers against future bailouts have proposed higher capital requirements for the biggest banks.

"I understand why policymakers and regulators and legislators don't want to be put in the situation they were in 2008," Stumpf said, adding that new regulations and current capital rules should be given "a chance to work."

While his firm won't buy other deposit-taking banks, mergers among smaller lenders may increase, Stumpf said.

"I would've thought you would've seen more activity by now," the CEO said. "It would not surprise me if you saw that pick up a bit."

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