Gere, who is in Japan to promote his latest movie, a Hollywood remake of the Japanese box-office hit "Shall We Dance," (search) accepted Koizumi's invitation, but insisted that he would lead.
"I'll be the man," Gere said before the two twirled for a few seconds in Koizumi's office.
Koizumi, who has been called "the Japanese Richard Gere" because of his resemblance to the American heartthrob, discussed his love of movies in a brief meeting with the actor. They also talked about their mutual affection for the ancient Japanese capital of Kyoto.
Gere, 55, told reporters afterward that the prime minister was "charming" and "spontaneous."
"It's a great honor for me to have the moments I've had with the prime minister. He's very generous," Gere said.
Koizumi, 63, lavished Gere with praise for being "interesting."
"He is a great person. Such a great movie star," Koizumi told the media at his daily news conference. "Wonderful person."
It's not the first time the media-savvy Koizumi has put on a performance with a Hollywood star. He and Tom Cruise sang a duet of Elvis Presley's "I Want You, I Need You, I Love You," when Cruise visited Japan to promote his movie "The Last Samurai."