  We explore the role of phase fluctuations in a 3-dimensional s-wave
superconductor, NbN, as we approach the critical disorder for the destruction
of the superconducting state. Scanning tunneling spectroscopy measurements
reveal that in the presence of strong disorder, a finite gap in the electronic
spectrum continues to persist at temperatures above Tc. With increase in
disorder, the superfluid density is strongly suppressed at low temperatures and
evolves towards a linear-T variation at higher temperatures. These observations
provide strong evidence that phase fluctuation leads to the formation of a
pseudogap state in a disordered conventional superconductor.
