X-ray line emission from 2l-nl' transitions in Ne-like Kr and nearby ions has been observed from approximately 1 microm Kr clusters irradiated by fs-scale laser pulses at the JAERI facility in Kyoto, Japan. The incident laser intensity reached 10(19) W/cm2, with pulse energies from 50 to 300 mJ and pulse durations from 30 to 500 fs. The dependence of the x-ray spectral features and intensity on the incident laser intensity is rather weak, indicating that the 1-2 ps cluster lifetimes limit the number of ions beyond Ne-like Kr that can be produced by collisional ionization. Lines from F- to Al-like Kr emitted from the cluster plasmas have been identified using data from the relativistic multiconfiguration flexible atomic code. A collisional-radiative model based on these data has been constructed and used to determine that the cluster plasma has electron densities near 10(22) cm(-3), temperatures of a few hundred eV, and hot electron fractions of a few percent.