A search for TeV-PeV muon neutrinos from unresolved sources was performed on AMANDA-II data collected between 2000 and 2003 with an equivalent live time of 807 days. This diffuse analysis sought to find an extraterrestrial neutrino flux from sources with nonthermal components. The signal is expected to have a harder spectrum than the atmospheric muon and neutrino backgrounds. Since no excess of events was seen in the data over the expected background, an upper limit of E2Φ90%C.L.<7.4×10-8GeVcm-2s-1sr-1 is placed on the diffuse flux of muon neutrinos with a Φ E-2 spectrum in the energy range 16 TeV to 2.5 PeV. This is currently the most sensitive Φ E-2 diffuse astrophysical neutrino limit. We also set upper limits for astrophysical and prompt neutrino models, all of which have spectra different from Φ E-2. © 2007 The American Physical Society.