We identify and evaluate a class of physical amplitudes in four-dimensional N = 4 superstring theory, which receive, in the weak-coupling limit, contributions of order e(-1/lambda), where lambda is the type II superstring coupling constant. They correspond to four-derivative (F) over tilde(1) interaction terms involving the universal type II dilaton supermultiplet. The exact result, obtained by means of a one-loop computation in the dual heterotic theory compactified on T-6, is compared with the perturbation theory on the type II side, and the e(-1/lambda) contributions are associated to non-perturbative effects of Euclidean solitons (D-branes) wrapped on K3 x T-2. The ten-dimensional decompactification limit on the type IIB side validates the recent conjecture for the D-instanton-induced R-4 couplings. (C) 1998 Elsevier Science B.V.