We derived photospheric parameters, mass-loss rates, and wind velocities of Galactic O6-O7 stars by analyzing high-resolution spectra in the far-UV and UV ranges with line-blanketed, hydrodynamic, non-LTE spherical models. We combined spectra from the Far Ultraviolet Spectroscopic Explorer (FUSE) in the range 905-1187 Å and International Ultraviolet Explorer (IUE) archival spectra (1150-3250 Å) and used the WM-BASIC code of Pauldrach et al. to compute model spectra. Lines in the FUSE range include high ionization stages (e.g., O VI) and lower abundance non-CNO elements (e.g., P V). Analyzed in addition to the N IV, N V, Si IV, and C IV lines in the IUE range, these features play a crucial role in uniquely constraining the stellar parameters, assessing the presence of shocks in the wind, and quantifying the effects of the resulting soft X-rays on the wind ionization. The effective temperatures derived from the consistent analysis of the far-UV and UV spectra are significantly (~6000 K or 15% on average, or between 4000 and 8000 K) lower than most values previously derived for some of our targets and lower than typical values assigned to their spectral types from different compilations. This result has great implications for our understanding of the evolution of massive stars and the characterization of young stellar populations, as well as for energy balance calculations of H II regions. Based on observations with the NASA-CNES-CSA Far Ultraviolet Spectroscopic Explorer, which is operated by The Johns Hopkins University under NASA contract NAS5-32985, and on IUE observations from the MAST and INES archives.