© Springer-Verlag 1996. Diffractive scattering of γ∗p → X + N, where N is either a proton or a nucleonic system with MN < 4 GeV has been measured in deep inelastic scattering (DIS) at HERA. The cross section was determined by a novel method as a function of the γ∗p c.m. energy W between 60 and 245 GeV and of the mass MX of the system X up to 15 GeV at average Q2 values of 14 and 31 GeV2. The diffractive cross section dσdi f f /dMX is, within errors, found to rise linearly with W. Parameterizing the W dependence by the form dσdi f f /dMX ∞ (W2)(2αIP - 2) the DIS data yield for the pomeron trajectory αIP = 1.23±0.02(stat)±0.04(syst) averaged over t in the measured kinematic range assuming the longitudinal photon contribution to be zero. This value for the pomeron trajectory is substantially larger than αIP extracted from soft interactions. The value of αIP measured in this analysis suggests that a substantial part of the diffractive DIS cross section originates from processes which can be described by perturbative QCD. From the measured diffractive cross sections the diffractive structure function of the proton F2D(3) (β,Q2, xIP) has been determined, where β is the momentum fraction of the struck quark in the pomeron. The form F2D(3) = constant·(1/xIP)a gives a good fit to the data in all β and Q2 intervals with a = 1.46 ± 0.04(stat) ± 0.08(syst).