We apply a modified phase-field modeling approach to the analysis of steps on a crystalline surface. Specifically, we are interested in capturing phenomena associated with the interaction between steps. To this end, we assign a physical significance to the form of the interfacial region between terraces (i.e. steps), inherent in the phase field approach, by tuning the multi-well potential to produce long-range interaction energies varying as 1/l (2), where l is half the distance between steps. Resultant repulsive interactions between adjacent steps of the same sign are shown to affect step-flow kinetics in a manner consistent with curvature-driven interfacial relaxation. This phenomenon is further demonstrated to cause dislocation-driven (spiral) crystal growth kinetics to deviate, for large supersaturation and Burgers vector values, from the classical quadratic growth law. Attractive interactions between adjacent steps of opposite sign, also resulting from the finite interfacial width, are briefly explored particularly with respect to their possible impact on two-dimensional nucleation.