Response matrix equations in two-dimensional geometry have been derived in the form of a set of coupled integral equations of the Fredholm type that have been solved by the moments method. The set of Legendre polynomials defined at the material interfaces has been chosen as the base for representing the partial interface currents and the response matrices. The method has been applied to the solution of the one-group diffusion equation and its convergence has been investigated in a series of numerical experiments, involving expansions of up to order 14. It turned out that the P1 approximation should be adequate for the majority of the two-dimensional problems occurring in power reactor design. Furthermore, the response method has a substantially higher computer efficiency than the finite difference method, both in processor time and in storage locations. As a by-product, the nature of the singularities around edges and corners of material interfaces has been analyzed by numerical experimentation.