Takahiro Hachigo made the comments to a small group of reporters after the official opening of a new plant in Wuhan.
Hachigo said that the catch-up could happen "soon", later clarifying to Reuters that he was referring to a two-to-three-year time 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's manufacturing capacity in China could be expanded if necessary, he added.
Honda last year sold roughly 1.7 million vehicles in the United States and 1.4 million in China.
(Reporting by Norihiko Shirouzu in Wuhan; writing by Yilei Sun in Shanghai; editing by Richard Pullin)