Nuclear reactions induced by a strong zeptosecond laser pulse are studied theoretically in the quasiadiabatic regime where the photon absorption rate is comparable to the nuclear equilibration rate. We find that multiple photon absorption leads to the formation of a compound nucleus in the so-far unexplored regime of excitation energies several hundred MeV above the yrast line. At these energies, further photon absorption is limited by neutron decay and/or induced nucleon emission. With a laser pulse of ≈ 50 zs duration, proton-rich nuclei far off the line of stability are produced.