A measurement of the proton structure function F2(x, Q2) is reported for momentum transfers squared Q2 between 4.5 GeV2 and 1600 GeV2 and for Bjorken x between 1.8 × 10-14 and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that F2 increases significantly with decreasing x, confirming our previous measurement made with one tenth of the data available in this analysis. The Q2 dependence is approximately logarithmic over the full kinematic range covered. The subsample of deep inelastic events with a large pseudo-rapidity gap in the hadronic energy flow close to the proton remnant is used to measure the "diffractive" contribution to F2. © 1995.