Ultraviolet laser emission is observed at room temperature in ZnO thin films consisting of hexagonal microcrystallites. At moderate pumping intensities, the optical gain responsible for lasing is shown to be due to an exciton-exciton collision process. At higher pumping intensities, optical gain due to EHP recombination radiation sets in and dominates the gain spectrum eventually. The exciton emission intensity is observed to depend on the size of the microcrystallites as a result of the weak confinement effect.