It is shown that focused wavefields satisfy a reciprocity principle concerning the roles of the focal point and the observation point. According to this principle, the diffracted field at a point P2of a converging spherical wave centred on the focal point P1is the complex conjugate of the diffracted field observed at P1if the focal point is at P2. The commonly used Debye integral representation of focused wavefields violates the reciprocity principle. Therefore we derive a new diffraction formula for focused wavefields which we call the modified Debye integral (MDI). It is constructed so as to satisfy the reciprocity principle, and may be considered as a generalization of the Debye integral and also as a refinement on a diffraction integral derived by Hopkins. For focusing of a two-dimensional perfect wave we show that the MDI gives the same f-number dependent parabolic phase factor on the geometrical focal line as is obtained numerically in the Kirchhoff approximation. For focusing of three-dimensional waves the MDI and the Kirchhoff theory are shown to predict the same focal shift in the paraxial approximation, as long as the shift is small compared with the focal distance.