A measurement of the proton structure function F2(x, Q2) is presented in the kinematic range 0.045 GeV2 < Q2 < 0.65 GeV2 and 6 · 10-7 < x < 1 · 10-3. The results were obtained using a data sample corresponding to an integrated luminosity of 3.9pb-1 in e+ p reactions recorded with the ZEUS detector at HERA. Information from a silicon-strip tracking detector, installed in front of the small electromagnetic calorimeter used to measure the energy of the final-state positron at small scattering angles, together with an enhanced simulation of the hadronic final state, has permitted the extension of the kinematic range beyond that of previous measurements. The uncertainties in F2 are typically less than 4%. At the low Q2 values of the present measurement, the rise of F2 at low x is slower than observed in HERA data at higher Q2 and can be described by Regge theory with a constant logarithmic slope δlnF2/δln(1/x). The dependence of F2 on Q2 is stronger than at higher Q2 values, approaching, at the lowest Q2 values of this measurement, a region where F2 becomes nearly proportional to Q2. (C) 2000 Elsevier Science B.V.