U.S. Bancorp's chairman and chief executive said the bank may have to cut jobs if interest rates don't rise as expected, a move the lender has resisted so far.

"If we're wrong and rates actually aren't going to move up…trust me, we will cut expenses," Richard Davis said at an investor conference in Manhattan on Thursday morning. Job cuts could be part of those expense cuts, he said.

There are no current plans to cut jobs, in part because the Minneapolis-based bank expects rates to start rising in September or December and because of the effect the move could have on morale, Mr. Davis said. The bank's head count was 67,000 in 2014, according to its annual report, a figure that was unchanged from the prior year.

Like other regional banks, U.S. Bancorp has faced a tough environment in which low interest rates have limited interest income and have pushed down net interest margin, a key profitability metric. Analysts say the bank currently has very low expenses when compared with its revenue.

Separately, Mr. Davis said the bank isn't eager to buy other banks, in part because of the regulatory and compliance risks. "I'll take pieces and parts, but not whole parts," he said.

For instance, the bank is interested in some of the assets being sold by General Electric Co. as a part of its plan to scale back its finance arm. But U.S. Bancorp would only pursue lines of business it is already in, Mr. Davis said.

Write to Rachel Louise Ensign at rachel.ensign@wsj.com

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