Retrieval-Augmented Generation (RAG) has emerged as a crucial approach for enhancing the responses of large language models (LLMs) with external knowledge sources. Despite the impressive performance in complex question-answering tasks, RAG still struggles with hallucinations. Attributing RAG-generated content through in-line citations has demonstrated potential in reducing hallucinations and facilitating human verification. Existing citation generation methods primarily rely on either fine-tuning the generator or employing post-processing approaches for citation matching. However, the former approach demands substantial annotated data and computational resources, while the latter often encounters difficulties in managing multiple citations and frequently produces suboptimal results. In this paper, we introduce a novel framework, called VeriCite, designed to rigorously validate supporting evidence and enhance answer attribution. Specifically, VeriCite breaks down into a three-stage generation: 1) The initial answer generation first generates a response based on all available contexts and has its claims verified through the NLI model; 2) the supporting evidence selection assesses the utility of each document and extracts useful supporting evidences; 3) the final answer refinement integrates the initial response and collected evidences to produce the final, refined answer.We conduct experiments across five open-source LLMs and four datasets, demonstrating that VeriCite can significantly improve citation quality while maintaining the correctness of the answers.