Large language models (LLMs) excel in generating unstructured text. However, they struggle with producing structured output while maintaining accuracy in zero-shot information extraction (IE), such as named entity recognition (NER) and relation extraction (RE). To address these challenges, we propose CROSSAGENTIE, a multi-agent framework that enhances zero-shot IE through multi-agent LLM collaboration. CROSSAGENTIE refines LLM predictions iteratively through two mechanisms: intra-group cross-type debate, which resolves entity-label conflicts through context-based evidence and confidence aggregation, and inter-group cross-task debate, where NER and RE mutually refine outputs via bidirectional feedback. Furthermore, we introduce template fine-tuning, distilling high-confidence multi-agent outputs into a single model, significantly reducing inference cost while preserving accuracy. Experiments across five NER and five RE datasets show that CROSSAGENTIE significantly outperforms state-of-the-art zero-shot baselines by a large margin. CROSSAGENTIE effectively addresses LLMs limitations in structured prediction with an effective and efficient approach for zero-shot information extraction.