We present a study of the topological susceptibility in lattice QCD with two degenerate flavors of dynamical quarks. The topological charge is measured on gauge configurations generated with a renormalization group improved gauge action and a mean held improved clover quark action at three values of beta = 6/g(2) with four sea quark masses at each beta. The lattice spacings at these beta 's are a approximate to 0.22, 0.16 and 0.11 fm at the physical up and down quark mass, which are fixed by the physical rho meson mass. The study is supplemented by simulations of pure SU(3) gauge theory with the same gauge action at 5 values of beta with lattice spacings 0.09 fm less than or similar toa less than or similar to0.27 fm. We employ a field-theoretic definition of the topological charge together with cooling. For the topological susceptibility in the continuum limit of pure SU(3) gauge theory we obtain chi (1/4)(t) = 197(-16)(+13) MeV where the error shows statistical and systematic ones added in quadrature, In full QCD chi (t) at heavy sea quark masses is consistent with that of pure SU(3) gauge theory. A decrease of chi (t) toward light quark masses, as predicted by the anomalous Ward-Takahashi identity for U(1) chiral symmetry, becomes clearer for smaller lattice spacings. The cross over in the behavior of chi (t) from heavy to light sea quark masses is discussed.