Takahiro Hachigo made the comments to a small group of reporters after the official opening of a new plant in Wuhan, which has boosted the Japanese carmaker's China production capacity to 1.2 million vehicles a year.
Hachigo said that the catch-up could happen "soon", later clarifying to Reuters that he was referring to a two-to-three-year period.
"We would like China sales to overtake the U.S.," he said, adding that the company did not expect U.S. sales to increase significantly.
Honda last year sold roughly 1.7 million vehicles in the United States and 1.4 million in China.
MANUFACTURING CAPACITY BOOST
China's car industry is facing a slowdown in sales as economic growth falters, and its auto market, world's largest, contracted last year for the first time since the 1990s.
Honda's business in China has been relatively strong, despite a quality issue that depressed sales in the first half of last year.
It is poised to grow further this year and beyond, in part because sales remain robust for most Japanese carmakers thanks in part to a thaw in bilateral relations between China and Japan. As a result, some Japanese automakers including Honda are trying to boost their presence in China.
Hachigo also said that Honda had the ability to further expand its China manufacturing capacity, though it would consider such a move carefully.
Wuhan is a major production hub for Honda, operated with its joint venture partner Dongfeng Group. It has a second China joint venture with GAC Group in the southern city of Guangzhou, where it has three plants capable of producing 600,000 vehicles a year.
(Reporting by Norihiko Shirouzu in Wuhan; writing by Yilei Sun in Shanghai; editing by Richard Pullin and Stephen Coates)
By Norihiko Shirouzu