Combining the superior optical properties of their bulk counterparts with quantum confinement effects, lead halide perovskite nanocrystals are unique laser materials with low-threshold optical gain. In such nonlinear optical regimes, multiple excitons are generated in the nanocrystals and strongly affect the optical gain through many-body interactions. Here, we investigate the exciton-exciton interactions in CsPbI3 nanocrystals by femtosecond transient absorption spectroscopy. From the analysis of the induced absorption signal observed immediately after the pump excitation, we estimated the binding energy for the hot biexcitons that are composed of an exciton at the band edge and a hot exciton generated by the pump pulse. We found that the exciton-exciton interaction becomes stronger for hot excitons with greater excess energies and that the optical gain can be controlled by changing the excess energy of the hot excitons.