Deep generative models have been the subject of immense interest in various fields of science. While seeking a molecule that favorably binds to a target is a long-established goal of drug design, various generative models have emerged to reach the goal. Here, we employ the concept of intermolecular interactions between a protein and a ligand in a 3D molecular generative model, empowering the generalizable structure-based drug design. Inspired by how the practitioners manage to improve the potency of a ligand toward a target protein, we devised a strategy where prior knowledge of appropriate interactions navigates the ligand generation. We thus propose an interaction-focused generative framework, which establishes a local interaction condition to capture the surrounding pocket environment. We demonstrate that the condition enables precise control of ligand generation, justifying its effectiveness in guiding a ligand design inside a binding pocket. Through this strategy, the generated ligands could stably bind to the target pocket by forming favorable interactions, regardless of pocket type. Furthermore, we highlight the broad applicability of our framework by leveraging the site-specific interaction condition suitable for designing ligands for various purposes.