We present the first measurement of cosmic-ray fluxes of Li6 and Li7 isotopes in the rigidity range from 1.9 to 25 GV. The measurements are based on 0.97 million Li6 and 1.04 million Li7 nuclei collected by the Alpha Magnetic Spectrometer on the International Space Station from May 2011 to October 2023. We observe that over the entire rigidity range the Li6 and Li7 fluxes exhibit nearly identical time variations and, above ∼4 GV, the time variations of Li6, Li7, He, Be, B, C, N, and O fluxes are identical. Above ∼7 GV, we find an identical rigidity dependence of the Li6 and Li7 fluxes. This shows that they are both produced by collisions of heavier cosmic-ray nuclei with the interstellar medium and, in particular, excludes the existence of a sizable primary component in the Li7 flux.