Uniqlo is having a tough time attracting customers in the U.S., where it has opened more than 40 stores from coast to coast.

"We're struggling now, but we're going to rebuild," Tadashi Yanai, the founder and head of Uniqlo owner Fast Retailing Co., told Reuters at an event in Tokyo on Wednesday. "People know us in places like New York. But we're not known in other areas. We would like people to know our products, our name, our way of thinking."

Yanai, who is Japan's richest man, also reportedly said he was traveling to the U.S. the same day and that the market is its "most important."

It's a notable admission given that the Japanese retailer, known for its colorful basic apparel, has been trying to make inroads with American shoppers for more than a decade now.