Static analyzers are vital to ensure software quality, but often produce false alarms; In this paper, we focus on the challenging task, directly refining defective static detection rules in the analyzer with Large Language Models to eliminate false positives/negatives fundamentally. This paper introduces RuleRefiner, a novel multi-stage framework for static analyzer rule refinement. RuleRefiner systematically employs LLMs by integrating dynamic profiling information for fact-based rule- code alignment, performing differential fault localization to ac-curately pinpoint error sources, and utilizing targeted templates to guide and constrain LLM-based modifications for precise and minimally disruptive enhancements. Evaluated on 218 real-world Semgrep rule issues, RuleRefiner achieved up to an 80.28% success rate, significantly outperforming baseline LLM methods by 1.34x-2.45x. Our results also demonstrate that RuleRefiner-refined rules are comparable, and sometimes superior, to expert-written ones in generalization and precision.