Deposit growth at JPMorgan Chase & Co., the largest U.S. bank by assets, is slowing as customers withdraw some of their money and stash it with competing banks that pay higher interest rates, a bank executive said Thursday.

Most big U.S. banks have been slow to raise the interest rates they pay customers on their savings and deposits, despite the U.S. Federal Reserve setting current rates at between 2.25% and 2.5%.

This has left an opening for some smaller and online-only banks that are trying to capitalize on customer frustration by offering savings accounts and other products that pay between 2% and 2.45% interest.

Gordon Smith, co-president and chief operating officer for JPMorgan Chase, said that though customers are taking out money, and this is contributing to slowing in the bank's deposit growth, most of those customers still keep Chase as their main bank.

"People are taking a component of their deposits. They're parking those deposits with a high-yield competitor, whomever they may be," said Smith, also head of JPMorgan's consumer and community banking.

"That money is very liquid," said Smith. "It'll then move from that high-yield competitor to another ... but that high-yield competitor is not winning the primary bank relationship, which is obviously what's critical."

Smith said the bank constantly reviews its deposit pricing and that interest rates are only part of what customers want from the bank.