Automated Program Repair (APR) aims to automatically generate correct patches for buggy programs. Recent approaches leveraging large language models (LLMs) have shown promise but face limitations. Most rely solely on static analysis, ignoring runtime behaviors. Some attempt to incorporate dynamic signals, but these are often restricted to training or fine-tuning, or injected only once into the repair prompt, without iterative use. This fails to fully capture program execution. Current iterative repair frameworks typically rely on coarse-grained feedback, such as pass/fail results or exception types, and do not leverage fine-grained execution-level information effectively. As a result, models struggle to simulate human stepwise debugging, limiting their effectiveness in multi-step reasoning and complex bug repair. To address these challenges, we propose DynaFix, an execution-level dynamic information-driven APR method that iteratively leverages runtime information to refine the repair process. In each repair round, DynaFix captures execution-level dynamic information such as variable states, control-flow paths, and call stacks, transforming them into structured prompts to guide LLMs in generating candidate patches. If a patch fails validation, DynaFix re-executes the modified program to collect new execution information for the next attempt. This iterative loop incrementally improves patches based on updated feedback, similar to the stepwise debugging practices of human developers. We evaluate DynaFix on the Defects4J v1.2 and v2.0 benchmarks. DynaFix repairs 186 single-function bugs, a 10% improvement over state-of-the-art baselines, including 38 bugs previously unrepaired. It achieves correct patches within at most 35 attempts, reducing the patch search space by 70% compared with existing methods, thereby demonstrating both effectiveness and efficiency in repairing complex bugs.