Self-assembly of membrane inclusions plays a key role in biological processes such as cellular signalling and trafficking and has potential applications for designing interfacial devices such as sensors and actuators. Despite intensive studies of curvature-mediated interactions, how membrane curvature modulates interactions between flat disk-like inclusions, adsorbed on vesicles, remains unknown. We use Monte Carlo simulations of a triangulated vesicle with simulated annealing to explore curvature-mediated interactions between disk-like rigid inclusions, induced by membrane elastic energy. We distinguish two distinct short and long-range curvature-mediated interactions for disk distances below and above the vesicle diameter. We observe short-range neutral interactions in the limit of small disks, where the vesicle appears as a flat bilayer to the disks. Beyond a certain size of disk-like inclusions, we find a transition from neutral to attractive short-range forces. Consistent with experiments, we also show that upon deflating vesicles, previously-attracted disks experience repulsive interactions. Our findings show how the vesicle curvature and the relative size between the disks and the vesicle determine the character of membrane-mediated interactions between adsorbed disk-like inclusions. Copyright © 2022 Alizadeh-Haghighi, Karaei Shiraz and Bahrami.