A measurement of the proton structure function F 2 (x, Q 2 ) is reported for momentum transfers squared Q 2 between 4.5 GeV 2 and 1600 GeV 2 and for Bjorken x between 1.8 10 - 4 and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that F 2 increases significantly with decreasing x, confirming our previous measurement made with one tenth of the data available in this analysis. The Q 2 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 F 2 .