"I asked her to play with the Orchestre de Paris and the Ensemble Orchestral de Paris on her next visit," the mayor told reporters. Rice has not yet given a response to the invitation, he added.
Rice, an accomplished pianist, performed with cellist Yo-Yo Ma when Ma was presented with the National Medal of the Arts in 2002.
During her trip to Paris, Rice visited the Hector Berlioz Conservatory and attended a student recital. The secretary was "very moved" by the performance, said Jean Dekyndt, the director of the conservatory.