This paper highlights that most existing conversational query rewriting research relies on an end-to-end approach, which struggles to simultaneously identify and rewrite multiple ambiguous expressions within a query. To address this, we propose a novel framework, Iterative Clarification and Rewriting (ICR), which performs iterative rewriting centered on query disambiguation. ICR alternates between generating disambiguation questions and rewriting them. Experimental results demonstrate that ICR consistently improves retrieval performance through this iterative process on two representative datasets, achieving state-of-the-art performance.