Scaling laws for magnetic minor hysteresis loops that are asymmetric and have their origin at an arbitrary point under a bias field have been examined for Fe single crystals with tensile deformation. We found that there exist power-law relations between field-dependent parameters of asymmetrical minor loops, which are the same as those for symmetrical ones observed previously. This agreement shows that the Bloch wall interaction with lattice defects is unchangeable irrespective of whether the Bloch walls move along the potential due to symmetrical or asymmetrical minor loops. The power-law relations were generalized on the basis of experimental results.