Exchange interactions in alpha- and gamma-Fe are investigated within an ab initio spin spiral approach. We have performed total-energy calculations for different magnetic structures as a function of lattice distortions, related to various cell volumes and the Bain tetragonal deformations. The effective exchange parameters in gamma-Fe are very sensitive to the lattice distortions, leading to the ferromagnetic ground state for the tetragonal deformation or increase of the volume cell. At the same time, themagnetic-structure-independent part of the total energy changes very slowly with the tetragonal deformations. The computational results demonstrate a strong mutual dependence of crystal and magnetic structures in Fe and explain the observable ``anti-Invar{''} behavior of thermal-expansion coefficient in gamma-Fe.