We show that certain heterotic string amplitudes are given in terms of correlators of the twisted topological (2,0) SCFT, corresponding to the internal sector of the N = 1 space-time supersymmetric background. The genus g topological partition function F g corresponds to a term in the effective action of the form W 2 g , where W is the gauge or gravitational superfield. We study also recursion relations related to holomorphic anomalies, showing that, contrary to the type II case, they involve correlators of anti-chiral superfields. The corresponding terms in the effective action are of the form W 2 g Π n , where Π is a chiral superfield obtained by chiral projection of a general superfield. We observe that the structure of the recursion relations is that of N = 1 spacetime supersymmetry Ward identity. We give also a solution of the tree-level recursion relations and discuss orbifold examples.