We derive a Supplemental evolution equation for a disclination line located on an interface between the uniaxial and isotropic phases of a nematic liquid crystal. This equation provides air additional kinetic relation accounting for the motion of art interfacial disclination line. In our treatment of the problem we neglect fluid motion. Our approach is based on the notion of configurational forces. To illustrate the role of our additional evolution equation, we consider two simple examples. We also identify an expression for the configurational force exerted by the uniaxial phase at the defect located on the phase interface. Published by Elsevier Inc.