A search for diffuse neutrinos with energies in excess of 10(5) GeV is conducted with AMANDA-II data recorded between 2000 and 2002. Above 10(7) GeV, the Earth is essentially opaque to neutrinos. This fact, combined with the limited overburden of the AMANDA-II detector ( roughly 1.5 km), concentrates these ultra-high-energy neutrinos at the horizon. The primary background for this analysis is bundles of downgoing, high-energy muons from the interaction of cosmic rays in the atmosphere. No statistically significant excess above the expected background is seen in the data, and an upper limit is set on the diffuse all-flavor neutrino flux of E-2 Phi(90%CL) < 2.7x10(-7) GeV cm(-2) s(-1) sr(-1) valid over the energy range of 2x10(5) to 10(9) GeV. A number of models that predict neutrino fluxes from active galactic nuclei are excluded at the 90% confidence level.