The surface detector array of the Pierre Auger Observatory can detect neutrinos with energy Eν between 1017 eV and 1020 eV from point-like sources across the sky south of +55° and north of –65° declinations. A search has been performed for highly inclined extensive air showers produced by the interaction of neutrinos of all flavors in the atmosphere (downward-going neutrinos), and by the decay of tau leptons originating from tau neutrino interactions in Earth's crust (Earth-skimming neutrinos). No candidate neutrinos have been found in data up to 2010 May 31. This corresponds to an equivalent exposure of ~3.5 years of a full surface detector array for the Earth-skimming channel and ~2 years for the downward-going channel. An improved upper limit on the diffuse flux of tau neutrinos has been derived. Upper limits on the neutrino flux from point-like sources have been derived as a function of the source declination. Assuming a differential neutrino flux kPSE–2ν from a point-like source, 90% confidence level upper limits for kPS at the level of ≈5 × 10–7 and 2.5 × 10–6 GeV cm–2 s–1 have been obtained over a broad range of declinations from the searches for Earth-skimming and downward-going neutrinos, respectively.