  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 \Ftilde_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.
