Certain scattering amplitudes in the gravitational sector of type II string theory on K3×T² are found to be computed by correlation functions of the N=4 topological string. This analysis extends the already known results for K3 by Berkovits and Vafa, which correspond to six-dimensional terms in the effective action, involving four Riemann tensors and 4g−4 graviphotons, R⁴T^4g−4, at genus g. We find two additional classes of topological amplitudes that use the full internal SCFT of K3×T². One of these string amplitudes is mapped to a 1-loop contribution in the heterotic theory, and is studied explicitly. It corresponds to the four-dimensional term R²(ddΦ)²T^2g−4, with Φ a Kaluza–Klein graviscalar from T². Finally, the generalization of the harmonicity relation for its moduli dependent coupling coefficient is obtained and shown to contain an anomaly, generalizing the holomorphic anomaly of the N=2 topological partition function F_g.