  We show that the strain-induced attraction between Abrikosov vortices has a
non-core contribution overlooked up until now. This contribution is an example
of the universal mechanism of soliton attraction in solids revealed in [Phys.
Rev. B {\bf 66}, 14111 (2002)]. The resulting interaction energy is larger than
that due to the vortex cores at least by a factor $\ln ^2 \kappa$.
Consequently, the non-core contribution must be included, for instance, in
discussions about the orientation of vortex lattices with respect to the
crystal axes. It is shown to be also important when interpreting the thermal
anomalies of the transition between superconducting and mixed states.
