Lately, they're "running out of money" at a faster clip, he said.

"We're seeing core consumers under a lot of pressure," Duke said at an event in New York. "There's no doubt that rising fuel prices are having an impact."

Wal-Mart's core shoppers are running out of money much faster than a year ago due to rising gasoline prices, and the retail giant is worried, CEO Mike Duke said Wednesday.

Wal-Mart shoppers, many of whom live paycheck to paycheck, typically shop in bulk at the beginning of the month when their paychecks come in.