Relational databases (RDBs) play a crucial role in many real-world web applications, supporting data management across multiple interconnected tables. Beyond typical retrieval-oriented tasks, prediction tasks on RDBs have recently gained attention. In this work, we address this problem by generating informative relational features that enhance predictive performance. However, generating such features is challenging: it requires reasoning over complex schemas and exploring a combinatorially large feature space, all without explicit supervision. To address these challenges, we propose ReFuGe, an agentic framework that leverages specialized large language model agents: (1) a schema selection agent identifies the tables and columns relevant to the task, (2) a feature generation agent produces diverse candidate features from the selected schema, and (3) a feature filtering agent evaluates and retains promising features through reasoning-based and validation-based filtering. It operates within an iterative feedback loop until performance converges. Experiments on RDB benchmarks demonstrate that ReFuGe substantially improves performance on various RDB prediction tasks. Our code and datasets are available at https://github.com/K-Kyungho/REFUGE.